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Tips, Formulae and shortcuts for Time, Speed, Distance & Work

Time, Speed, Distance and Work Tips by CRACKU.IN

• Time, Distance and Work is the most important topic for all

Competitive examinations.

• The questions from this topic varies from easy to difficult.

• This formula sheet covers the most importance tips that

helps you to answer the questions in a easy, fast and accurate way.

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While converting the Speed in m/s to km/hr, multiply it by 3.6.

It is because 1 m/s = 3.6 km/hr

Cracku Tip 1 – Time, Speed, Distance & Work

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If the ratio of the speeds of A and B is a : b, then

• The ratio of the times taken to cover the same distance is 1/a : 1/b

or b : a.

• The ratio of distance travelled in equal time intervals is a : b

Cracku Tip 2 – Time, Speed, Distance & Work

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Cracku Tip 3 – Time, Speed, Distance & Work

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• If D1 km is travelled at speed of S1 km/hr, and D2 km is travelled at speed of S2 km/hr then,

Average Speed = km/hr

Cracku Tip 4 – Time, Speed, Distance & Work

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Cracku Tip 5 – Time, Speed, Distance & Work

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Let the distances travelled in each part of the journey be d1, d2, d3 and so on till dn and the speeds in each part be s1, s2, s3 and so on till sn.

If d1 = d2 = d3 =...= dn= d, then the average speed is the harmonic mean of the speeds s1, s2, s3 and so on till sn.

Constant time :

Let the distances travelled in each part of the journey be d1, d2, d3 and so on till dn and the time taken for each part be t1, t2, t3 and so on till tn.

If t1 = t2 = t3 =...= tn= t, then the average speed is the arithmetic mean of the speeds s1, s2, s3 and so on till sn.

Cracku Tip 6 – Time, Speed, Distance & Work

Constant distance :

Clocks

In a well functioning clock, both the hands meet after every

720 / 11 Mins.

It is because relative speed of minute hand with respect to hour hand = 11/2 degrees per minute.

Cracku Tip 6 – Time, Speed, Distance & Work

Cracku Tip 7 – Time, Speed, Distance & Work

Circular Tracks

If two people are running on a circular track with speeds in ratio a:b where a and b are co-prime, then • They will meet at a+b distinct points if they are running in

opposite direction.

• They will meet at |a-b| distinct points if they are running in same

direction

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Cracku Tip 8 – Time, Speed, Distance & Work

Circular Tracks

If two people are running on a circular track having perimeter l, with speeds m and n,

• The time for their first meeting = l / (m +n)

(when they are running in opposite directions)

• The time for their first meeting = l / (|m-n|)

(when they are running in the same direction)

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If a person P starts from A and heads towards B and another person Q starts from B and heads towards A and they meet after a time 't' then,

t = √(x*y) where x = time taken (after meeting) by P to reach B and y = time taken (after meeting) by Q to reach A.

Cracku Tip 9 – Time, Speed, Distance & Work

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Cracku Tip 10 – Time, Speed, Distance & Work

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Cracku Tip 11 – Time, Speed, Distance & Work

Trains

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Cracku Tip 12 – Time, Speed, Distance & Work

WORK:

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The direction along the stream is called downstream. And, the direction against the stream is called upstream.

Cracku Tip 13 – Time, Speed, Distance & Work

BOATS & STREAMS

If the speed of water is 'W' and speed of a boat in still water is 'B‘ • Speed of the boat (downstream) is B+W • Speed of the boat (upstream) is B-W

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Cracku Tip 14 – Time, Speed, Distance & Work

BOATS & STREAMS

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Cracku Tip 15 – Time, Speed, Distance & Work

PIPES & CISTERNS:

Cracku Tip 16 – Time, Speed, Distance & Work

• Some of the questions may consume a lot of time. While solving, write down the equations as far as possible to avoid mistakes. The few extra seconds can help you avoid silly mistakes.

• Check if the units of distance, speed and time match up. So if you

see yourself adding a unit of distance like m to a unit of speed m/s, you would realize you have missed a term.

• Choose to apply the concept of relative speed wherever possible as

it can greatly reduce the complexity of the problem.

• Like speed and distance, in time and work while working with terms

ensure that you convert all terms to consistent units like man-hours.

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Important Time, Speed, Distance & Work Questions

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QuestionsInstructionsFor the following questions answer them individually

Question 1

Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 metres. To do a favour to Arjun, Karan starts 10 metres behind thestarting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with thesecond race?

A Karan and Arjun reach the finishing line simultaneously.

B Arjun beats Karan by 1 metre

C Arjun beats Karan by 11 metres.

D Karan beats Arjun by 1 metre.Answer: D

Video Solution

Explanation:The speeds of Karan and Arjun are in the ratio 10:9. Let the speeds be 10s and 9s.Time taken by Karan to cover 110 m = 110/10s = 11/sTime taken by Arjun to cover 100 m = 100/9s = 11.11/sTherefore, Karan reaches the finish line before Arjun. From the options, the only possible answer is d).

Question 2

Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hourrespectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arundid Kiranmala start?

A 3

B 3.5

C 4

D 4.5

E 5Answer: C

Video Solution

Explanation:Let the distance be D.Time taken by Arun = D/30Time taken by Barun = D/40Now, D/40 = D/30 - 2=> 3D = 4D - 240=> D = 240Therefore time taken by Arun to cover 240 km = 240/30 = 8 hrTime Kiranmala takes to cover 240 km = 240/60 = 4 hrSo, Kiranmala has to start 4 hours after Arun.

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Question 3

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the samedistance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then takeonly 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

A

B

C

D

Answer: D

Video Solution

Explanation:

=> and => and => => => => =>

Take 3 Free CAT Mocks (With Solutions) Question 4

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps forevery two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pacelets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many stepswould they have to take to walk up?

A 40

B 50

C 60

D 80Answer: B

Video Solution

Explanation:Let the number of steps on the escalator be x.

So, by the time Shyama covered 25 steps, the escalator moved 'x-25' steps.

Hence, the ratio of speeds of Shyama and escalator = 25:(x-25)

Similarly, the ratio of speeds of Vyom and escalator = 20:(x-20)

But the ratio is 3:2

37

34

35

38

12/(R − S) = T

12/(R + S) = T − 612/(2R − S) = t

12/(2R + S) = t − 112/(R − S) − 12/(R + S) = 6 12/(2R − S) − 12/(2R + S) = 112R + 12S − 12R + 12S = 6R −2 6S2 24R + 12S − 24R + 12S = 4R −2 S2

24S = 6R −2 6S and24S =2 4R −2 S2

6R −2 6S =2 4R −2 S2

2R =2 5S2

24S = 10S −2 S =2 9S2

S = 24/9 = 8/3

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Ratio of speeds of Shyama and Vyom = 25(x-20)/20*(x-25) = 3/2

=> 10(x-20) = 12(x-25)

=> 2x = 100 => x = 50

Question 5

There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’s still the potatoes and gravy, yams,salad, and cranberries, not to mention setting the table.

Three friends — Asit, Arnold and Afzal — work together to get all of these chores done. The time it takes them to do the work togetheris 6 hr less than Asit would have taken working alone, 1 hr less than Arnold would have taken alone, and half the time Afzal would havetaken working alone. How long did it take them to do these chores working together?

A 20 min

B 30 min

C 40 min

D 50 minAnswer: C

Video Solution

Explanation:Let the time taken working together be t.Time taken by Arnold = t+1Time taken by Asit = t+6Time taken by Afzal = 2t

Work done by each person in one day =

Total portion of workdone in one day

or

Therefore total time = hours = 40mins

Alternatively,

From the options, if time min, that is,

LHS =

RHS = The equation is satisfied only in case of option CHence, C is correct

Question 6

On a 20 km tunnel, connecting two cities A and B, there are three gutters (1, 2 and 3). The distance between gutters 1 and 2 is half thedistance between gutters 2 and 3. The distance from city A to its nearest gutter, gutter 1, is equal to the distance of city B from gutter3. On a particular day, the hospital in city A receives information that an accident has happened at gutter 3. The victim can be savedonly if an operation is started within 40 min. An ambulance started from city A at 30 km/hr and crossed gutter 1 after 5 min. If the driverhad doubled the speed after that, what is the maximum amount of time would the doctor get to attend to the patient at the hospital.

Assume that a total of 1 min is elapsed for taking the patient into and out of the ambulance?

A 4 minB 2.5 min

+(t+1)1

+(t+6)1

2t1

= t1

+(t+1)1

+(t+6)1

=2t1

t1

+(t+1)1

=(t+6)1

2t2−1

2t + 7 = 2t(t+1)⋅(t+6)

3t −2 7t + 6 = 0 ⟶ t = 32

t = −3

32

+(t+1)1

+(t+6)1

=2t1

t1

= 40 t = 32

+53

+203

=43

=20(12+3+15)

=2030

23

=t1

23

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C 1.5 min

D The patient died before reaching the hospitalAnswer: C

Video Solution

Explanation:Let the distance between gutter 1 and A be x and between gutter 1 and 2 be y.

Hence, x + y + 2y + x = 20 => 2x+3y=20

Also x = 30kmph * 5/60 = 2.5km

Hence, y = 5km

After the ambulance doubles its speed it goes at 60kmph i.e. 1km per min. Hence, time taken for the rest of the journey = 15*2 + 2.5 =32.5

It takes 1 min to load and unload the patient.

Hence, total time = 5 + 32.5 + 1 = 38.5 mins

So, the doctor would get 1.5 min to attend to the patient.

CAT Previous Papers PDFQuestion 7

It takes six technicians a total of 10 hr to build a new server from Direct Computer, with each working at the same rate. If sixtechnicians start to build the server at 11 am, and one technician per hour is added beginning at 5 pm, at what time will the server becompleted?

[CAT 2002]

A 6.40 pm

B 7 pm

C 7.20 pm

D 8 pmAnswer: D

Video Solution

Explanation:Let the work done by each technician in one hour be 1 unit.Therefore, total work to be done = 60 units.From 11 AM to 5 PM, work done = 6*6 = 36 units.Work remaining = 60 - 36 = 24 units.Work done in the next 3 hours = 7 units + 8 units + 9 units = 24 units.Therefore, the work gets done by 8 PM.

Question 8

Three small pumps and a large pump are filling a tank. Each of the three small pump works at 2/3 the rate of the large pump. If all fourpumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

[CAT 2002]

A 4/7

B 1/3

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C 2/3

D 3/4Answer: B

Video Solution

Explanation:Let the work done by the big pump in one hour be 3 units.Therefore, work done by each of the small pumps in one hour = 2 units.Let the total work to be done in filling the tank be 9 units.Therefore, time taken by the big pump if it operates alone = 9/3 = 3 hours.If all the pumps operate together, the work done in one hour = 3 + 2*3 = 9 units.Together, all of them can fill the tank in 1 hour.Required ratio = 1/3

Question 9

A car after traveling 18 km from a point A developed some problem in the engine and speed became 4/5 of its original speed As aresult, the car reached point B 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then itwould have reached B only 36 minutes late. The original speed of the car (in km per hour) and the distance between the points A and B(in km.) is

A 25, 130

B 30,150

C 20, 90

D None of theseAnswer: D

Video Solution

Explanation:Time difference, when second time car's engine failed at a distance of 30 km., is of 9 min.Hence putting this in equation:

hr. (Because difference of time is considered with extra travelling of 12 km. in second case)

We will get km/hr.

Now for distance hr. (As car is 45 min. late after engine's faliure in first case)So = 78 km. Hence none of these will be our answer.

Free CAT Exam Preparation AppQuestion 10

Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B istwice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. Howmuch time will be required to produce a million units if all the three machines are used simultaneously?

A 12 hours

B 10 hours

C 8 hours

D 6 hour

−54v12

=v12

609

v(velocity) = 20

+16d−18

−2018

=20d

6045

d

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Answer: B

Video Solution

Explanation:As machine B's efficiency is twice as of A's, Hence, it will complete its work in 30 hours.

And C's efficiency is putting A and B together i.e. = 20 hours Now if all three work together, then it will be completed in x (say) days.

or x = 10 hours

Question 11

Every day Neera's husband meets her at the city railway station at 6.00 p.m. and drives her to their residence. One day she left earlyfrom the office and reached the railway station at 5.00 p.m. She started walking towards her home, met her husband coming from theirresidence on the way and they reached home 10 minutes earlier than the usual time. For how long did she walk?

A 1 hour

B 50 minutes

C 1/2 hour

D 55 minutesAnswer: D

Video Solution

Explanation:Since we know that Neera's husband drives at a uniform speed to and from his residence.If he saved 10 mins overall travel time, he should have driven 5 mins less towards railway station and 5 mins less while driving towardsresidence.If he saved 5 minutes in his return journey, he should have started to return 5 minutes before his actual return time.When the husband met Neera, he should have met her 5 minutes before the actual meeting time i.e. at 5.55 PM. So, Neera must have walked for 55 minutes from 5PM.

Question 12

In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then whoout of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (Onemile is 1,600 m.)

A Akshay, mile

B Chinmay, mile

C Akshay, mile

D Chinmay, mileAnswer: D

Video Solution

Explanation:Akshay can complete 1600 - 128 = 1472 m and Bhairav can completer 1600 m in the same time.

Bhairav can complete 100 m and Chinmay can complete 96 m in the same time.

=> Bhairav can complete 1600 m and Chinmay can complete 1536 m in the same time.

(( +601

) )301 −1

=x1

+201

+301

601

121

321

241

161

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=> Akshay can complete 1472 m and Chinmay can complete 1536 m in the same time.

1.5 miles => 2400 m

Distance travelled by Akshay by the time Chinmay completes 1.5 miles = = 2300 m

=> Akshay lost by 100 m, which is of a mile.

CAT Formulas PDF [Download Now]Question 13

A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and restsfor 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-Dare all equal to 12 km, the time for which he rested at B could be

A 3 hr

B 6 hr

C 2 hr

D 4 hrAnswer: A

Video Solution

Explanation:Total time taken to reach at D:

Or

From the options we can see that only, = 3hr satisfies the equation. Thus, A is the right choice.

Question 14

Three wheels can complete 60, 36 and 24 revolutions per minute. There is a red spot on each wheel that touches the ground at timezero. After how much time, all these spots will simultaneously touch the ground again?

A s

B s

C sD sAnswer: C

Video Solution

Explanation:

The first wheel completes a revolution in second

The second wheel completes a revolution in second

The third wheel completes a revolution in second

The three wheels touch the ground simultaneously at time which are multiples of the above three times.

Hence, the required number is seconds.

So, the correct option is option (c)

∗15361472

2400

th161

+x12

x + +2x12

2x + =4x12

16

3x −2 16x + 21 = 0

x

25

35

5

7.5

=6060

1

=3660

1 32

=2460

2 21

LCM(1, , ) =35

25

5

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Question 15

The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportionalto the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9compartments are attached, the maximum number of compartments that can be carried by the engine is:

A 49

B 48

C 46

D 47Answer: B

Video Solution

Explanation:The function of the speed of the train = 42 - k where n is the number of compartments and k is a constant.

42 - k = 24

=> 3k = 18 => k = 6

=> Function of speed = 42 - 6

Speed is 0 when 42 - 6 = 0

=> 42 = 6

=> n = 49

=> So, with a positive speed, the train can carry 48 compartments.

Top-500 Free CAT Questions (With Solutions)Question 16

Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50km per hour towards Baroda situated100 kms away. At 7:00 am Howrah - Ahmedabad express leaves Baroda towards Ahmedabad and travels at 40 km per hour. At 7:30Mr. Shah, the traffic controller at Baroda realises that both the trains are running on the same track. How much time does he have toavert a head-on collision between the two trains?

A 15 minutes

B 20 minutes

C 25 minutesD 30 minutesAnswer: B

Video Solution

Explanation:The distance between Ahmedabad and Baroda is 100 KmNavjivan express starts at 6:30 am at 50 Km/hr and Howrah expresses starts at 7:00 am at 40 Km/hr.Distance covered by Navjivan express in 30 minutes (by 7 am) is 25 Km/hr.

So, at 7 am, the distance between the two trains is 75 Kms and they are travelling towards each other a relative speed of 50+40=90Km/hr.

So, time taken them to meet is 75/90*60 = 50 minutes.

As, Mr. Shah realizes the problem after thirty minutes, time left to avoid collision is 50-30 = 20 minutes

n

9

n

n

n

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Question 17

A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete thejob in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the sameefficiency joins the work. How many days are required to complete the job?

Answer:15

Video Solution

Explanation:Let the rate of work of a person be x units/day. Hence, the total work = 120x.

It is given that one first day, one person works, on the second day two people work and so on.

Hence, the work done on day 1, day 2,... will be x, 2x, 3x, ... respectively.

The sum should be equal to 120x.

n = 15 is the only positive solution.

Hence, it takes 15 days to complete the work.

Question 18

A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. Ifinstead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. Thedistance (in km) from his home to the railway station is

Answer:20

Video Solution

Explanation:We see that the man saves 20 minutes by changing his speed from 12 Km/hr to 15 Km/hr.

Let d be the distance

Hence,

d = 20 Km.

Free CAT Study MaterialQuestion 19

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of hismotor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

A

B

C

D 3:2Answer: B

120x = x ∗ 2n(n+1)

n +2 n − 240 = 0

−12d

=15d

31

=60d

31

:6 2

:7 2

2 :5 3

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Video Solution

Explanation:Let the speed of the river be and the speed of the boat be . Let be the one way distance and be the initial time taken.

Given,

... i

Also,

... ii

Equating both i and ii,

+ =

Question 20

In a 10 km race, A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. I f A beats B by 1 kmand B beats C by 1 km, then by how many metres does A beat C?

Answer:1900

Video Solution

Explanation:By the time A traveled 10 KM, B traveled 9 KMHence Similarly Hence Hence by the time A traveled 10 KMs , C should have traveled 8.1 KMsSo A beat C by 1.9 KMs = 1900 Mts

Question 21

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles perhour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by himis

A 55 miles

B 60 miles

C 65 miles

D 70 milesAnswer: C

Video Solution

Explanation:

x u d t

t = +u−xd

u+xd

=4t

+2u−xd

2u+xd

t = +2u−x4d

2u+x4d

u − x

d

u + x

d

+2u − x

4d

2u + x

4d

=u − x2 22u

4u − x2 216u

4u −2 x =2 8u −2 8x2

=x2u2

47

=xu

27

Speed :A Speed =B 10 : 9Speed :B Speed =C 10 : 9

Speed :A Speed :B Speed =C 100 : 90 : 81

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Let the distance between the home and office be miles

Time taken for going in the morning = hrs

Time taken for going back in the evening = . hrsIt is given that he took 30 minutes (0.5 hrs) more in the evening

Hence hrs + 0.5 = Solving for x, we get x = 15 miles.Total distance traveled = 2x + x + x + 5 = 4x + 5 = 65 Miles

Free CAT Preparation Video LecturesQuestion 22

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipeis open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomeshalf-full?

A 20

B 30

C 40

D 45Answer: A

Video Solution

Explanation:Let the time taken by the outlet pipe to empty = x hours

Then, => Hence time taken by the outlet pipe to make the tank half-full = 40/2 = 20 hour

Question 23

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towardspoint A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. Whatis the distance, in km, between A and B7

A 364B 378

C 380

D 388Answer: B

Video Solution

Explanation:Let the distance traveled by the car be x KMsDistance traveled by the bike = 168 KMsSpeed of car is double the speed of bike

=> =

=> = => x = 210 Hence the distance between A and B is x + 168 = 378 KMs

2x

602x

+25x

50x+5

602x

+25x

50x+5

−81

=x1

101

x = 40

3:40−2:00x

2 × 3:40−1:00168

100x

2 × 160168

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Question 24

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 daysand are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal'sshare, in rupees, is

A 100

B 200

C 300

D 400Answer: A

Video Solution

Explanation:Let the time take by kamal to complete the task be x days.

Hence we have => x = 40 days.

Ratio of the work done by them = = 4 : 5 : 1Hence the wage earned by Kamal = 1/10 * 1000 = 100

Daily Free CAT Practice TestsQuestion 25

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirtydays to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteenhumans working together (without any robot) take to finish it?

A 45

B 36

C 32

D 40Answer: C

Video Solution

Explanation:Let the efficiency of humans be 'h' and the efficiency of robots be 'r'.In the first case, Total work = (15h + 5r) * 30......(i)In the second case,Total work = (5h + 15r) * 60......(ii)On equating (i) and (ii), we get(15h + 5r) * 30 = (5h + 15r) * 60Or, 15h + 5r = 10h + 30rOr, 5h = 25rOr, h = 5rTotal work = (15h + 5r) * 30 = (15h + h) * 30 = 480h

Time taken by 15 humans = days= 32 days.

Hence, option C is the correct answer.

+101

+81

=x1

41

:101

:81

401

15h480h

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Question 26

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B.Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is halfthat of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

Answer:12

Video Solution

Explanation:Let the distance between A and B be 4x. Length of BP is thrice the length of AP.=> AP = x and BP = 3x

Let the speed of car 1 be s and the speed of car 2 be 0.5s. Car 2 reaches P one hour (60 minutes) after Car 1 reaches P.

=> x/s + 60 = 3x/0.5sx/s + 60 = 6x/s5x/s = 60x/s = 12

Time taken by car 1 in reaching P from A = x/s = 12 minutes.Therefore, 12 is the correct answer.

Question 27

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The twotrains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours doestrain T take for its journey from X to Y?

Answer:15

Video Solution

Explanation:Train T starts at 3 PM and train S starts at 4 PM. Let the speed of train T be t.=> Speed of train S = 0.75t.

When the trains meet, train t would have traveled for one more hour than train S. Let us assume that the 2 trains meet x hours after 3 PM. Trains S would have traveled for x-1 hours.

Distance traveled by train T = xtDistance traveled by train S = (x-1)*0.75t = 0.75xt-0.75t

We know that train T has traveled three fifths of the distance. Therefore, train S should have traveled two-fifths the distance between the2 cities.

=> (xt)/(0.75xt-0.75t) = 3/22xt = 2.25xt-2.25t0.25x = 2.25x = 9 hours.

Train T takes 9 hours to cover three-fifths the distance. Therefore, to cover the entire distance, train T will take 9*(5/3) = 15 hours. Therefore, 15 is the correct answer.

CAT Syllabus (Download PDF)

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Question 28

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: Aworks alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5%of the job. In how many days can B alone finish the entire job?

A 20

B 22

C 16

D 18Answer: A

Video Solution

Explanation:Let us assume that A can complete 'a' units of work in a day and B can complete 'b' units of work in a day. A works alone till half the work is completed. A and B work together for 4 days and B works alone to complete the last 5% of the work. => A and B in 4 days can complete 45% of the work.

Let us assume the total amount of work to be done to be 100 units.4a + 4b = 45 ---------(1)B needs 25% more time than A to finish a job. => 1.25*b = a ----------(2)

Substituting (2) in (1), we get, 5b+4b = 459b = 45b = 5 units/day

B alone can finish the job in 100/5 = 20 days. Therefore, option A is the right answer.

Question 29

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hoursmore than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed ofPartha, in km per hour, is

A 6

B 4

C 3

D 5Answer: D

Video Solution

Explanation:Let the time taken by Partha to cover 60 km be x hours.Narayan will cover 60 km in x-4 hours.

Speed of Partha =

Speed of Narayan =

x60

x−460

Downloaded from cracku.in

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Partha reaches the mid-point of A and B two hours before Narayan reaches B.

=>

Partha will take 12 hours to cross 60 km.

=> Speed of Partha = Kmph.Therefore, option D is the right answer.

Question 30

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at thesame rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hourswhen 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two fillingpipes are on?

Answer:10

Video Solution

Explanation:Let the efficiency of filling pipes be 'x' and the efficiency of draining pipes be '-y'.In the first case, Capacity of tank = (6x - 5y) * 6..........(i)In the second case,Capacity of tank = (5x - 6y) * 60.....(ii)On equating (i) and (ii), we get (6x - 5y) * 6 = (5x - 6y) * 60or, 6x - 5y = 50x - 60yor, 44x = 55yor, 4x = 5yor, x = 1.25y

Capacity of the tank = (6x - 5y) * 6 = (7.5y - 5y) * 6 = 15yNet efficiency of 2 filling and 1 draining pipes = (2x - y) = (2.5y - y) = 1.5y

Time required = hours = 10 hours.

Hence, 10 is the correct answer.

Free Videos for CAT PreparationQuestion 31

A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, whenopen, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B areopen, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filledif 7 inlets of type A and 27 inlets of type B are open?

Answer:48

Video Solution

Explanation:Let the efficiency of type A pipe be 'a' and the efficiency of type B be 'b'.In the first case, 10 type A and 45 type B pipes fill the tank in 30 mins.

+x6030

2 =(x−4)

6060

+2x

2 = x − 4

=2x+4

x − 4x + 4 = 2x − 8x = 12

=1260

5

1.5y15y

1Downloaded from cracku.in

.

So, the capacity of the tank = (10a + 45b)........(i)

In the second case, 8 type A and 18 type B pipes fill the tank in 1 hour.So, the capacity of the tank = (8a + 18b)..........(ii)Equating (i) and (ii), we get10a + 45b = 16a + 36b=>6a = 9bFrom (ii), capacity of the tank = (8a + 18b) = (8a + 12a) = 20aIn the third case, 7 type A and 27 type B pipes fill the tank.Net efficiency = (7a + 27b) = (7a + 18a) = 25a

Time taken = hour = 48 minutes.

Hence, 48 is the correct answer.

Question 32

Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets car 1 at Q, and car 2at P. If each car is moving in uniform speed then the ratio of the speed of car 2 to that of car 1 is

A 2 : 7

B 2 : 9

C 1 : 2

D 1 : 4Answer: D

Video Solution

Explanation:Car 3 meets car 1 at Q, which is 200 km from A.Therefore, at the time of their meeting car 1 must have travelled 200 km and car 3 must have travelled 100 km.As the time is same, ratio of speed of car 1 to speed of car 3 = 2 : 1.

Car 3 meets car 2 at P, which is 100 km from A.Therefore, at the time of their meeting car 2 must have travelled 100 km and car 3 must have travelled 200 km.As the time is same, ratio of speed of car 2 to speed of car 3 = 1 : 2.

Speed of car 1 : speed of car 3 = 2 : 1And speed of car 2 : speed of car 3 = 1 : 2So, speed of car 1 : speed of car 2 : speed of car 3 = 4 : 1 : 2

Hence, option D is the correct answer.

Question 33

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank isfull. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, Aalone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if bothpumps were used simultaneously all along?

A 4:48 pm

B 4:12 pm

C 4:24 pm

D 4:36 pmAnswer: C

21

25a20a

Downloaded from cracku.in

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Video Solution

Explanation:Let 't' pm be the time when the tank is emptied everyday. Let 'a' and 'b' be the liters/hr filled by pump A and pump B respectively.

On Monday, A alone completed filling the tank at 8 pm. Therefore, we can say that pump A worked for (8 - t) hours. Hence, the volume ofthe tank = a*(8 - t) liters.

Similarly, on Tuesday, B alone completed filling the tank at 6 pm. Therefore, we can say that pump B worked for (6 - t) hours. Hence, thevolume of the tank = b*(6 - t) liters.

On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. Therefore, we can say that pump Aworked for (5 - t) hours and pump B worked for 2 hours. Hence, the volume of the tank = a*(5 - t)+2b liters.

We can say that a*(8 - t) = b*(6 - t) = a*(5 - t) + 2b

a*(8 - t) = a*(5 - t) + 2b

3a = 2b ... (1)

a*(8 - t) = b*(6 - t)

Using equation (1), we can say that

Therefore, we can say that the tank gets emptied at 2 pm daily. We can see that A takes 6 hours and pump B takes 4 hours alone.

Hence, working together both can fill the tank in = \dfrac{6*4}{6+4} = 2.4 hours or 2 hours and 24 minutes.

The pumps started filling the tank at 2:00 pm. Hence, the tank will be filled by 4:24 pm.

CAT Percentile PredictorQuestion 34

Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Eachcar travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance,in km, between car 2 and B when car 1 reaches B is

Answer:5

Video Solution

Explanation:

Time taken to cover first 50 km at 100 km/hr = hr.Time taken to cover second 50 km at 50 km/hr = 1 hr.Time taken to cover last 50 km at 25 km/hr = 2 hr.When car 2 starts, car 1 has already covered 20 km.So, time taken by car 1 to reach B after car 1 starts = total time - time required to travel first 20 km= 3 hr 30 min - 12 min = 3 hr 18 minDistance travelled by car 2 = (50 + 50 + 45) = 145 kmDistance from B = (150 - 145) km = 5 km

Hence, 5 is the correct answer.

Question 35

Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and hisefficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Rameshgot sick, in how many days would he have completed the remaining work?

A 14.5

B 11

⇒

a ∗ (8 − t) = ∗23a

(6 − t)

t = 2

21

Downloaded from cracku.in

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C 13.5

D 12Answer: C

Video Solution

Explanation:Let 'R' and 'G' be the amount of work that Ramesh and Ganesh can complete in a day.

It is given that they can together complete a work in 16 days. Hence, total amount of work = 16(R+G) ... (1)

For first 7 days both of them worked together. From 8th day, Ramesh worked at 70% of his original efficiency whereas Ganesh worked athis original efficiency. It took them 17 days to finish the same work. i.e. Ramesh worked at 70% of his original efficiency for 10 days.

16(R+G) = 7(R+G)+10(0.7R+G)

16(R+G) = 14R+17G

R = 0.5G ... (2)

Total amount of work left when Ramesh got sick = 16(R+G) - 7(R+G) = 9(R+G) = 9(0.5+G) = 13.5G

Therefore, time taken by Ganesh to complete the remaining work = = 13.5 days.

Question 36

On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from Bat the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs.The difference between their speeds, in km per hour, is

Answer:50

Video Solution

Explanation:

Let 'a' and 'b' be the speed (in km/hr) of cars starting from both A and B respectively.

If they both move in east direction, then B will catch A if and only if b > a.

Relative speed of both the cars when they move in east direction = (b - a) km/hr

It takes them 7 hours to meet. i.e. they travel 350 km in 7 hours with a relative speed of (b-a) km/hr.

Hence, (b - a) = = 50 km/hr.

Important Verbal Ability Questions for CAT (Download PDF)Question 37

Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meetfor the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

A 10:25 am

B 10:45 am

⇒

⇒

⇒

G

13.5G

7350

Downloaded from cracku.in

.

C 10:18 am

D 10:27 amAnswer: D

Video Solution

Explanation:When A and B met for the first time at 10:00 AM, A covered 60% of the track.

So B must have covered 40% of the track.

It is given that A returns to P at 10:12 AM i.e A covers 40% of the track in 12 minutes

60% of the track in 18 minutes

B covers 40% of track when A covers 60% of the track.

B covers 40% of the track in 18 minutes.

B will cover the rest 60% in 27 minutes, hence it will return to B at 10:27 AM

Question 38

A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B.Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how manymotorcycles would have reached B by the time the cyclist reached B?

A 22

B 23

C 15

D 20Answer: C

Video Solution

Explanation:It is given that starting from 10:01 am, every minute a motorcycle leaves A and moves towards B.

Forty-five such motorcycles reach B by 11 am.

It means that the forty-fifth motorcycle starts at 10:45 AM at A and reaches B by 11:00 AM i.e 15 minutes.

Since the speed of all the motorcycles is the same, all the motorcycles will take the same duration i.e 15 minutes.

If the cyclist doubles the speed, then he will reach B by 10:30 AM. (Since if the speed is doubled, time is reduced by half)

Since each motorcycle takes 15 minutes to reach B, 15 motorcycles would have reached B by the time the cyclist reaches B

Question 39

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While Johnmakes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A?

Answer:48

Video Solution

Explanation:Speed of John = 6kmph

Speed of Mary = 7.5 kmph

Lengths of tracks A and B = 325 m

Downloaded from cracku.in

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Let the length of track A be a, then the length of track B = 325-a

9 rounds of John on track A = 5 rounds of Mary on track B

On solving we get , 13a=1300

a=100

The length of track A = 100m, track B = 225m

Mary makes one round of track A =

= 48 sec

Data Interpretation for CAT Questions (download pdf)Question 40

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again,after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days wasthe job done?

A 12

B 13

C 15

D 14Answer: B

Video Solution

Explanation:Let the total work be LCM of 20, 40 = 40 units

Efficiency of Anil and Sunil is 2 units and 1 unit per day respectively.

Anil works alone for 3 days, so Anil must have completed 6 units.

Bimal completes 10% of the work while working along with Anil and Sunil.

Bimal must have completed 4 units.

The remaining 30 units of work is done by Anil and Sunil

Number of days taken by them 30/3=10

The total work is completed in 3+10=13 days

Question 41

Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their commondestination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage bywhich the speed of the second car could exceed that of the first car is

A 20

B 30

C 25

D 10Answer: A

= 6 × 18 5 9× a

7.5× 18 5

5⋅ 325−a( )

7.5× 18 5 100

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Video Solution

Explanation:Let the speed of cars be a and b and the distance =d

Minimum time taken by 1st car = 6 hours,

For maximum difference in time taken by both of them, car 1 has to start at 10:00 AM and car 2 has to start at 11:00 AM.

Hence, car 2 will take 5 hours.

Hence a= and b =

Hence the speed of car 2 will exceed the speed of car 1 by = = 20

Question 42

The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was

A

B

C

D

Answer: C

Video Solution

Explanation:Distance covered by A in 1 revolution = 2 *30 = 60

Distance covered by B in 1 revolution = 2 *40 = 80

Now, (5000+n)60 = 80 n

=> 15000= 4n-3n =>n=15000

Then distance travelled by B = 15000*80 cm = 12 km

Hence, the speed = = 16

Logical Reasoning for CAT Questions (download pdf)Question 43

In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres,what was the length, in metres, of the racecourse?

Answer:880

Video Solution

Explanation:Assuming the length of race course = x and the speed of three horses be a,b and c respectively.

Hence, ......(1)

and ......(2)

Also, ......(3)

6 d

5 d

× 6 d

− 5 d

6 d

100 × 6 d

30 d

100

18π

14π

16π

12π

π π

π π

π π

π π

45 12π× 60

π

= a x

b x−11

= a x

c x−90

= b x

c x−80

x−11 x−90Downloaded from cracku.in

.

From 1 and 2, we get, .....(4)

Dividing (3) by (4), we get,

=> (x-11)(x-80)=x(x-90)

=> 91x-90x=880 => x=880

Question 44

One can use three different transports which move at 10, 20, and 30 kmph, respectively to reach from A to B. Amal took each mode of

transport for of his total journey time, while Bimal took each mode of transport for of the total distance. The percentage bywhich Bimal’s travel time exceeds Amal’s travel time is nearest to

A 22

B 20

C 19

D 21Answer: A

Video Solution

Explanation:Assume the total distance between A and B as d and time taken by Amal = t

Since Amal travelled of his total journey time in different speeds

d =

Hence, the ratio of time taken by Bimal to time taken by Amal =

Therefore, Bimal will exceed Amal's time by

Question 45

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and Bhad worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take tofinish the task if she works alone at her usual efficiency?

A 36

B 24

C 18

D 12Answer: C

Video Solution

Explanation:Assuming A completes a units of work in a day and B completes B units of work in a day and the total work = 1 unit

Hence, 12(a+b)=1.........(1)

Also, 9( +3b)=1 .........(2)

= b x−11

c x−90

= x x−11

x−80 x−90

31 rd

31 rd

31 rd

× 3 t

10 + × 3 t

20 + × 3 t

30 = 20t

Total time taken by Bimal = +s1

d1

+s2

d2s3

d3

= × 320t

+101

× 320t

+201

× 320t

=301

=3 ×3020t 6+3+2( )

t911

=t9

11t

911

× t

−t9 11t

100 = 22.22

2 a

a

Downloaded from cracku.in

.

Using both equations, we get, 12(a+b)= 9( +3b)

=> 4a+4b= +9b

=> =5b

=> a=2b

Substituting the value of b in equation (1),

12( )=1

=> a=

Hence, the number of days required = 1/( )=18

Quantitative Aptitude for CAT Questions (download pdf)Question 46

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If twomachines can finish the job in 13 days, then how many men can finish the job in 13 days?

Answer:13

Video Solution

Explanation:Consider the work done by a man in a day = a and that by a machine = b

Since, three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job,hence the efficiency will be double.

=> 3a+8b = 2(3b+8a)

=> 13a=2b

Hence work done by 13 men in a day = work done by 2 machines in a day.

=> If two machines can finish the job in 13 days, then same work will be done 13 men in 13 days.

Hence the required number of men = 13

Question 47

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. Aftermeeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60km/hr, then the speed of Car 2, in km/hr, is

A 100

B 90

C 80

D 70Answer: B

Video Solution

Explanation:Let the speed of Car 2 be 'x' kmph and the time taken by the two cars to meet be 't' hours.

In 't' hours, Car 1 travels while Car 2 travels

It is given that the time taken by Car 1 to travel is 45 minutes or (3/4) hours. or ....(i)

2 a

2 3a

2 5a

2 3a

18 1

18 1

60 × t km( ) x × t km( )

x × t km( ) ∴ = 60x × t( )

43

t = 4x180

60× t( ) 1 xDownloaded from cracku.in

.

Similarly, the time taken by Car 2 to travel is 20 minutes or (1/3) hours. or ....(ii)

Equating the values in (i) and (ii), and solving for x:

Hence, Option B is the correct answer.

Question 48

Leaving home at the same time, Amal reaches the office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr.Leaving home at 9.10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10 am?

A 13

B 12

C 14

D 11Answer: B

Video Solution

Explanation:

The difference in the time take to traverse the same distance at two different speeds is 35 minutes. Equating this:

On solving, we obtain . Let be the speed at which Amal needs to travel to reach the office in 50 minutes; then

.Hence, Option B is the correct answer.

Know the CAT Percentile Required for IIM CallsQuestion 49

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its returnjourney, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage bywhich the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

A 50

B 58

C 67

D 61Answer: C

Video Solution

Explanation:Let the total distance be 'D' km and the speed of the train be 's' kmph. The time taken to cover D at speed d is 't' hours. Based on the

information: on equating the distance, we get

On solving we acquire the value of or 15 mins. We understand that during the return journey, the first 5 minutes are spenttraveling at speed 's' {distance traveled in terms of s = }. Remaining distance in terms of 's' =

The rest 4 minutes of stoppage added to this initial 5 minutes amounts to a total of 9 minutes. The train has to complete the rest of the

journey in or {1/10 hours}. Thus, let 'x' kmph be the new value of speed. Based on the above, we get

60 × t km( ) ∴ =x60× t( )

31 ∴ t = 180

x

∴ =4x180

⟶ 180x

x = 90 kmph

d′ ′ −8d

= 15d

6035

d = 10kms xkmph

=x10

or x = 6050

12 kmph

s × t = × 3s

t +( 21)

t = 41

12s

−4s

=12s

6s

15 − 9 = 6mins =x6s

or x =101

610s

−s( 10s )Downloaded from cracku.in

.

Since the increase in speed needs to be calculated: increase.

Hence, Option C is the correct answer.

Question 50

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came frombehind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post isnearest to

A 87

B 82

C 78

D 75Answer: B

Video Solution

Explanation:Let the length of the train be and speed be . Base on the two scenarios presented, we obtain:

....(i) and ...(ii)

On dividing (ii) by (i) and simplifying we acquire the value of as . Substituting this value in (i), we have {keeping it in km and hours for convenience}

Since we need to find , let this be equal to . Then,

Hence, Option B is the correct choice.

Question 51

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Answer:40

Video Solution

Explanation:Let the desired efficiency of each worker '6x' per day.

140*6x*200= 6 km ...(i)

In 60 days 60/200*6=1.8 km of work is to be done but actually 1.5km is only done.

Actual efficiency 'y'= 1.5/1.8 *6x =5x.

Now, left over work = 4.5km which is to be done in 140 days with 'n' workers whose efficiency is 'y'.

=> n*5x*140=4.5 ...(ii)

(i)/(ii) gives,

=> n=180.

.'. Extra 180-140 =40 workers are needed.

Join MBA Telegram Group

× s

−s( 610s )

100 = ≈ 3200

67%

lkms skmph

=s−2l

360090

=s−4l

3600100

s 22kmph l = × 360090

20 kms

sl

x x = 90 × =2220

81.81 ≈ 82 sec onds

=n⋅5x⋅140( )140⋅6x⋅200( )

4.56

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.

Question 52

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual total time to reachoffice, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly ontime is

A 29

B 26

C 28

D 27Answer: C

Video Solution

Explanation:Let distance = d

Given,

=> d = 28km

The actual time taken to travel 28km = 28/40 = 7/10 hours = 42 min.

Given time taken to travel 58/3 km = 1/3 *42 = 14 min.

Then a break of 8 min.

To reach on time, he should cover remaining 28/3 km in 20 min => Speed = km/hr

Question 53

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another trainleaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

A 11 : 45 am

B 11 : 20 am

C 11 : 00 am

D 10 : 45 amAnswer: C

Video Solution

Explanation:The distance travelled by A between 9:00 Am and 10:30 Am is 3/2*40 =60 km.

Now they are separated by 30 km

Let the time taken to meet =t

Distance travelled by A in time t + Distance travelled by B in time t = 30

40t + 20t =30 => t=1/2 hour

Hence they meet at 11:00 AM

−35d

=40d

606

=6020

( 328 )

28

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Question 54

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwisedirection. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Aniland Sunil meet again for the first time at the starting point?

A 4.8

B 4.6

C 5.2

D 4.2Answer: A

Video Solution

Explanation:

Anil and Sunil will meet at a first point after LCM ( ) = 3/5 hr

In the mean time, distance travelled by ravi = 8 * 3/5 = 4.8 km

Enroll for Excellent CAT/MBA coursesQuestion 55

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to thattaken by train 2 in travelling from A to C is

A 5:7

B 4:1

C 1:4D 7:5Answer: A

Video Solution

Explanation:Let the distance from A to B be "x", then the distance from B to C will be 3x. Now the speed of Train 2 is double of Train 1. Let the speedof Train 1 be "v", then the speed of Train 2 will be "2v" while travelling from A to B.

Time taken by Train 1 = (x/v)

Time taken by Train 2 = (x/2v)

Now from B to C distance is "3x" and the speed of Train 2 is (v) and the speed of Train 1 is (2v).

Time taken by Train 1 = 3x/2v

Time taken by Train 2 = 3x/v

Total time taken by Train 1 = x/v(1+(3/2)) = (5/2)(x/v)

Total time taken by Train 2 = x/v(3+(1/2))= (7/2)(x/v)

Ratio of time taken =

,153

103

=2725

75

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Question 56

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than Johntakes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them workingtogether. In how many days will Jim finish the job working alone?

Answer:4

Video Solution

Explanation:Let Jack take "t" days to complete the work, then John will take "2t" days to complete the work. So work done by Jack in one day is (1/t)and John is (1/2t) .

Now let Jim take "m" days to complete the work. According to question, Hence Jim takes "2t" timeto complete the work.

Now let the three of them complete the work in "p" days. Hence John takes "p+3" days to complete the work.

or m=1. Hence JIm will take (1+3)=4 days to complete the work. Similarly John will also take 4 days to complete the work

Question 57

In a car race, car A beats car B by 45 km. car B beats car C by 50 km. and car A beats car C by 90 km. The distance (in km) over whichthe race has been conducted is

A 475

B 450

C 500

D 550Answer: B

Video Solution

Explanation:Now car A beats car B by 45km. Let the speed of car A be v(a) and speed of car B be v(b).

.....(1)where '"m" is the entire distance of the race track.

Moreover .......(2)

and finally ......(3)

Multiplying (1) and (2) we get (3).

Solving we get m=450 which is the length of the entire race track

Cracku CAT Success StoriesQuestion 58

A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other. Ram andRahim reach their destination in one minute and four minutes, respectively. if they start at the same time, then the ratio of Ram's speedto Rahim's speed is

+t1

=m1

or =2t3

m1

or m =2t 1

2t

m + 3 =2t1

( ) m(2t4

)

m + 3 =2t1

( ) m(2t4

)

=v b( )v a( )

m−45m

=v c( )v b( )

m−50m

=v c( )v a( )

m−90m

=m−90m

m−45m

(m−50m

)

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A

B

C

D

Answer: C

Video Solution

Explanation:Let the speed of Ram be v(r) and the speed of Rahim be v(h) respectively. Let them meet after time "t" from the beginning.

Hence Ram will cover v(r)(t) during that time and Rahim will cover v(h)t respectively.

Now after meeting Ram reaches his destination in 1 min i.e. Ram covered v(h)t in 1 minute or v(r)(1)= v(h)(t)

Similarly Rahim reaches his destination in 4 min i.e. Rahim covered v(r)t in 4 minutes or v(h)(4)= v(r)(t)

Dividing both the equations we get Hence the ratio is 2.

Question 59

Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram andRahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ramwill make before he meets Rahim again for the first time is

A 5

B 3

C 2

D 4Answer: B

Video Solution

Explanation:

To complete one round Ram takes 100m/15kmph and Rahim takes 20m/5kmph

They meet for the first time after L.C.M of (100m/15kmph , 20m/5kmph) = 100m/5kmph=20m/kmph.

Distance traveled by Ram =20m/kmph * 15kmph =300m.

So, he must have ran 300/100=3 rounds.

Note:

21

2

2

2 2

=4v h( )v r( )

or =v r( )v h( )

v h( )v r( )

2

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CAT gave both 2 and 3 as correct answers because of the word ' before'.

Question 60

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long andcrosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is

A 184

B 192

C 190

D 180Answer: C

Video Solution

Explanation:

Speed of the faster train = m/s

Speed of the slower train = m/s

Sum of speeds (when the trains travel towards each other) = m/s

Let the slower train be metres long; then:

On solving,

Subscribe to MBA Exams Youtube ChannelQuestion 61

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only onalternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number ofdays needed to complete the work is

A 5B 8

C 6

D 7Answer: D

Video Solution

Explanation:Let the total amount of work be 60 units.

Then Anu, Vinu, and Manu do 4, 5, and 3 units of work per day respectively.

On the 1st day, Anu and Vinu work. Work done on the 1st day = 9 units

On the 2nd day, Manu and Vinu work. Work done on the 2nd day = 8 units

This cycle goes on. And in 6 days, the work completed is 9+8+9+8+9+8 = 51 units.

On the 7th day, again Anu and Vinu work and complete the remaining 9 units of work. Thus, the number of days taken is 7 days.

=12160

340

−340

6 × =( 185

) 335

+340

=335

25

x =25160+x

14

x = 190 m

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Question 62

Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar andAnthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor theslowest works alone, the time in months he will take to complete the project is

Answer:32

Video Solution

Explanation:Let the total work be 48 units. Let Amar do 'm' work, Akbar do 'k' work, and Anthony do 'n' units of work in a month.

Amar and Akbar complete the project in 12 months. Hence, in a month they do =4 units of work.

m+k = 4.

Similarly, k+n = 3, and m+n = 2.

Solving the three equations, we get .

Here, Amar works neither the fastest not the slowest, and he does 1.5 units of work in a month. Hence, to complete the work, he would

take months.

Question 63

Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to crosseach other. The ratio of length of train A to that of train B is

A 3:2

B 5:3

C 2:3

D 2:1Answer: A

Video Solution

Explanation:Considering the length of train A = La, length of train B = Lb.

The speed of train A be 5*x, speed of train B be 3*x.

From the information provided :

The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other.

In this case, train A traveled a distance equivalent to the length of train B which is Lb at a speed of 5*x+3*x = 8*x because both the trainsare traveling in the opposite direction.

Hence (8*x)*(46) = Lb.

In the information provided :

It took another 69 seconds for the rear ends of the trains to cross each other.

In the next 69 seconds

The train B traveled a distance equivalent to the length of train A in this 69 seconds.

Hence (8*x)*(69) = La.

La/Lb = 69/46 = 3/2 = 3 : 2

Join CAT 2022 Online Coaching

1248

m = , k =23

, n =25

21

=1.548

32

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.

Question 64

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him.Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR,proportionate to the work done by him, is

A 9000

B 9200

C 9100

D 9150Answer: C

Video Solution

Explanation:Let Entire work be W Now Anil worked for 24 days Bimal worked for 14 days and Charu worked for 14 days .Now Anil Completes W in 60 days so in 24 days he completed 0.4W Bimal completes W in 84 Days

So in 14 Days Bimal completes =

Therefore work done by charu = = =

Therefore proportion of Charu = =9100

Question 65

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipeB is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then thetank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is

A 144

B 140C 264D 120Answer: A

Video Solution

Explanation:Let A fill the tank at x liters/hour and B drain it at y liters/hour Now as per Condition 1 : We get Volume filled till 10pm = 8x-7y (1) .Here A operates for 8 hours and B operates for 7 hours .As per condition 2We get Volume filled till 6pm = 4x-2y (2)Here A operates for 4 hours and B operates for 2 hours .Now equating (1) and (2) we get 8x-7y =4x-2yso we get 4x =5y y =4x/5

So volume of tank =

So time taken by A alone to fill the tank = = 144 minutes

6W

W − −6W

104W

1026W

3013W

× 3013

21000

8x − 7 × =54x

512x

=x5

12x

hrs 512

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Question 66

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Workingalone, the time Rahul would have taken, in hours, to complete the work is

A 11.5

B 10

C 12.5

D 12Answer: B

Video Solution

Explanation:Let Rahul work at a units/hr and Gautam at b units/hourNow as per the condition :8a+6b =7.5a+7.5bso we get 0.5a=1.5bor a=3bTherefore total work = 8a +6b = 8a +2a =10aNow Rahul alone takes 10a/10 = 10 hours.

Take 3 Free CAT Mocks (With Solutions) Question 67

Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactlyafter 3 minutes. The number of rounds Mira walks in one hour is

Answer:8

Video Solution

Explanation:Considering the distance travelled by Mira in one minute = M,

The distance traveled by Amal in one minute = A.

Given if they walk in the opposite direction it takes 3 minutes for both of them to meet. Hence 3*(A+M) = C. (1)

C is the circumference of the circle.

Similarly, it is mentioned that if both of them walk in the same direction Amal completes 3 more rounds than Mira :

Hence 45*(A-M) = 3C. (2)

Multiplying (1)*15 we have :

45A + 45M = 15C.

45A - 45M = 3C.

Adding the two we have A =

Subtracting the two M =

Since Mira travels in one minute, in one hour she travels :

Hence a total of 8 rounds.

Alternatively,

9018C

9012C

9012C

⋅9012C

60 = 8C

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Let the length of track be L and velocity of Mira be a and Amal be b Now when they meet after 45 minutes Amal completes 3 more rounds than Mira so we can say they met for the 3rd time moving in the same direction so we can say they met for the first time after 15 minutes So we know Time to meet = Relative distance /Relative velocity

so we get (1)Now When they move in opposite directionThey meet after 3 minutes

so we get (2)Dividing (1) and (2)

we get or 4a =6b or a = 3b/2Now substituting in (1) we get :

so

So we can say 1 round is covered in hours so in 1-hour total rounds covered = 8.

Question 68

Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then theamount in INR received by him is

Answer:3000

Video Solution

Explanation:Now Anil Paints in 12 Days Barun paints in 16 Days Now together Arun , Barun and Chandu painted in 6 Days Now let total work be W Now each worked for 6 days So Anil's work = 0.5W

Barun's work =

Therefore Charu's work =

Therefore proportion of charu =

Take 3 Free CAT Mocks (With Solutions)

CAT Previous Papers PDF

Free CAT Exam Preparation App

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Top-500 Free CAT Questions (With Solutions)

=6015

a−bL

=603

a+bL

=a−b( )a+b( )

5

× bL

2 = 6015

=bL

81

81

=166W

83W

−2W

= 83W

8W

= 824000

3, 000

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