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Mathematics Miscellaneous Quiz Q1. In a village the average age of n people is 42 years. But after the verification it was found that

the age of a person had been considered 20 years less than the actual age, so the new average,

after the correction, increased by 1. The value of n is:

(a) 21

(b) 20

(c) 22

(d) None of these

Q2. The average rainfall in the months of January and February is 6 cm and in the months of

March to June is 5 cm and July to October is 10 cm and in the November and December, it is 6 cm.

The average rainfall for the whole year is:

(a) 7

(b) 5.5

(c) 7.5

(d) None of these

Q3. On an average 300 people watch the movie in Sahu Cinema hall on Monday, Tuesday and

Wednesday and the average number of visitors on Thursday and Friday is 250. If the average

number of visitors per day in the week be 400, then the average number of people who watch the

movie in weekends (i.e., on Saturday and Sunday) is:

(a) 500

(b) 600

(c) 700

(d) None of these

Q4. The average salary is being paid to all its employees by

the Biotech corporation is Rs. 15,500. The average salary of

the senior employees is Rs. 18000 per month and the average

salary of the junior employees is Rs. 12,000 per month. If

there are only two levels of employees viz junior and senior

level, then what fraction of the total employees is the junior

level employees are:

(a) 7

10

(b) 5

12

(c) 5

10

(d) None of these

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Q5. The average income of A, B and C is Rs. 12,000 per month and the average income of B, C and D

is Rs. 15,000 per month. If the average salary of D be twice that of A, then the average salary of B

and C is (in Rs.):

(a) 8,000

(b) 18,000

(c) 13,500

(d) 9,000

Q6. A travel agency has three types of vehicles viz. four seater, autorickshaw, 10 seater maxi cab

and 20 seater minibus. The rate of each passenger (irrespective of its age or weight or seniority)

for the auto rickshaw is Rs. 12 and for the maxi cab is Rs. 15 and for the minibus is Rs. 8 for the

one round. The average occupancy of the seats is 100%, 80% and 75% respectively. If he has only

one vehicle of each kind, then the average earning for one round of each vehicle is:

(a) Rs. 96

(b) Rs. 90

(c) Rs. 86

(d) Rs. 70

Q7. The average age of all the 100 employees in an office is 29 years, where 2/5 employees are

ladies and the ratio of average age of men to women is 5 : 7. The average age of female employees

is:

(a) 18 years

(b) 35 years

(c) 25 years

(d) None of these

Q8. In a particular week the average number of people who visited the Tajmahal is 40. If we

exclude the holidays then the average is increased by 16. Further if we exclude also the day on

which the maximum number of 112 people visited the Tajmahal, then the average becomes 42.

The number of holiday in the week is:

(a) 1

(b) 2

(c) 3

(d) Data insufficient

Q9. In a combined family the average age of 4 males and 7 females is 42 and 20 years respectively.

If two persons whose average age is 13 years have left the family and other three people joined

the family whose respective ages are 11, 15 and 28 years, then the average age of the new family is

increased by:

(a) 4 years

(b) 1 year

(c) 3 years

(d) None of these

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Q10. There are 6 consecutive odd numbers in increasing order. The difference between the

average of the squares of the first 4 numbers and the last four numbers is 64. If the sum of the

squares of the first and the last element (i.e., odd numbers) is 178, then the average of all the six

numbers is:

(a) 7

(b) 8

(c) 9

(d) 10

Q11. A naughty student breaks the pencil in such a way that the ratio of two broken parts is same

as that of the original length of the pencil to one of the large part of the pencil. The ratio of the

other part to the original length of pencil is:

(a) 1 : 2√5

(b) 2 : (3 + √5)

(c) 2 : √5

(d) Can’t be determined

Q12. A student obtained equal marks in History and Sociology. The ratio of marks in Sociology and

Geography is 2 : 3 and the ratio of marks in History and Philosophy is 1 : 2. If he has scored an

aggregate of 55% marks. The maximum marks in each subject it same. In how many subjects did

he score equal to or greater than 60% marks?

(a) 1

(b) 2

(c) 3

(d) None of these

Q13. The ratio of income of Anil and Mukesh is 2 : 3. The sum of their expenditure is Rs. 8000 and

the amount of savings of Anil is equal to the amount of expenditure of Mukesh. What is the sum of

their savings?

(a) 22,000

(b) 4,000

(c) 16,000

(d) 12,000

Q14. Hutch and Essar entered into a partnership just 5 months

ago. The ratio of profit claimed by Hutch and Essar is 6 : 17. If

Essar had just started his business 12 months ago with Rs. 1275,

what is the amount contributed by Hutch?

(a) Rs. 980

(b) Rs. 1080. (c) Rs. 1200. (d) Rs. 998

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Q15. The concentration of petrol in three different mixtures (petrol and kerosene) is 𝟏

𝟐,

𝟑

𝟓 and

𝟒

𝟓

respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed.

What is the ratio of petrol and Kerosene in the new mixture?

(a) 4 : 5

(b) 3 : 2

(c) 3 : 5

(d) 2 : 3

Q16. There are two vessels containing the mixture of milk and water. In the first vessel the water

is 2/3 of the milk and in the second vessel water is just 40% of the milk. In what ratio these are

required to mix to make 24 litres mixture in which the ratio of water is to milk is 1 : 2?

(a) 4 : 3

(b) 5 : 7

(c) 5 : 2

(d) 7 : 5

Q17. 6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same

tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a UHSA pump?

(a) 6 : 7

(b) 7 : 6

(c) 7 : 54

(d) Can’t be determined

Q18. The ratio of prices of Cello and Rotomac pens in 2000 were in the ratio of 3 : 5. In 2005 the

price of Cello pen trebles itself and the price of Rotomac pen is increased by Rs. 100, then the new

ratio of prices of the same pens becomes 4 : 5. What was the original price of the Rotomac pen in

2000?

(a) Rs. 60

(b) Rs. 80

(c) Rs. 100

(d) Rs. 120.

Q19. A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3 and another tin contains the

Dew and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to

achieve a perfect proportion of 2 : 1 (in which Dew is 2 times that of sprite).

(a) 10 : 3

(b) 4 : 1

(c) 3 : 10

(d) 3 : 1

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Q20. Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4:1. When his naughty

child crushed these grapes, then some water get wasted. Now the ratio of water is to pulp is 3 : 2.

What is the total amount of the crushed grapes?

(a) 0.5 kg

(b) 1 kg

(c) 0.75 kg

(d) None of these

Q21. An aircraft was to take off from a certain airport at 8 a.m. but it was delayed by 30 minutes.

To make up for the lost time, it was to increase its speed by 250 km/hr from the normal speed to

reach its destination 1500 km away, on time. What was the normal speed of the aircraft?

(a) 650 km/hr

(b) 750 km/hr

(c) 850 km/hr

(d) 10000 km/hr

Q22. If a child walks at the rate of 5 m/min from his home, he is 6 minutes late for school; if he

walks at the rate of 7 m/min, he reaches half an hour earlier. How far is his school from his home?

(a) 450 metres

(b) 540 metres

(c) 630 metres

(d) 360 metres

Q23. A car driver driving in fog, passes a pedestrian who was walking at the rate of 2 km/hr in the

same direction. The pedestrian could see the car for 6 minutes and it was visible to him upto a

distance of 0.6 km. The speed of the car would be:

(a) 8 km/hr

(b) 800 m/hr

(c) 200 m/hr

(d) 15 km/hr

Q24. Two stations A and B are 110 km apart on a straight line.

One train starts from ‘A’ at 7 am and travel towards ‘B’ at 20

km/hr speed. Another train starts for ‘B’ at 8 am and travel

towards ‘A’ at 25 km/hr speed. At what time will they meet?

(a) 9 a.m.

(b) 10 a.m.

(c) 11 a.m.

(d) None of these

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Q25. A constable follows a thief who is 200 m ahead of the constable. If the constable and the thief run at speed of 8 km/hr and 7 km/hr respectively, the constable would catch the thief in? (a) 10 minutes (b) 12 minutes (c) 15 minutes (d) 20 minutes Q26. ABCD is a cyclic parallelogram. The ∠B is equal to: (a) 30° (b) 60° (c) 45° (d) 90° Q27. From four corners of a square sheet of side 4 cm, four pieces, each in the shape of arc of a circle with radius 2 cm, are cut out. The area of the remaining portion is: (a) (8 – π) sq.cm (b) (16 – 4π) sq.cm (c) (16 – 8π) sq.cm (d) (4 – 2π) sq.cm Q28. On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC ?

(a) 7.5 (b) 7 (c) 7.75 (d) None of these Q29. P, Q, S, R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR ?

(a) 2𝑟(1 + √3)

(b) 2𝑟(2 + √3)

(c) 𝑟(1 + √5)

(d) 2𝑟 + √3 Q30. AB is a chord to a circle and PAT is the tangent to the circle at A. If ∠BAT = 75° and ∠BAC = 45°, C being a point on the circle, then ∠ABC is equal to: (a) 40° (b) 45° (c) 60° (d) 70°

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Solutions

S1. Ans.(b) Sol. Sum of ages = 42 n sum of ages + 20

n= 43

42 n + 20 = 43 n n = 20 S2. Ans.(a) Sol. Average Rain fall

=6 × 2 + 5 × 4 + 4 × 10 + 6 × 2

12

=12 + 20 + 40 + 12

12=

84

12= 7

S3. Ans.(c) Sol. Total no. of people on Saturday & Sunday = 400 × 7 – 300 × 3 – 250 × 2 = 2800 – 900 – 500 = 1400 Average no. of people on Sunday & Saturday = 1400/2 = 700 S4. Ans.(b) Sol. Using Alligation

Total Employees = 7 + 5 = 12r Junior Employees = 5r

Fraction = 5

12

S5. Ans.(c) Sol. A + B + C = 12000 × 3 = 36000 …(i) B + C + D = 15000 × 3 = 45000 …(ii) From (i) & (ii) D – A = 9000 D = 2A (Given) 2A – A = 9000 A = 9000 9000 + B + C = 36000 B + C = 36000 – 9000 B + C = 27000

Average = B + C

2=

27000

2 = 13500 Rs.

Senior Junior

18000 12000

15500

3500 : 2500

7 : 5

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S6. Ans.(a)

Sol. Earning from autorickshaw for 1 round= 4 × 12 = 48 Rs.

Earning from Maxi cab for 1 round= 10 × 80

100 × 15= 120 Rs.

Earning from minibus= 20 ×75

100× 8= 120 Rs.

Average earning=120+120+48

3=

288

3= 96 Rs.

S7. Ans.(b)

Sol. Total Employees = 100

Female = 100 × 2

5 = 40

Male = 60

Ratio of Average age of Male + female = 5 : 7

Average age of Male ⇒ 5x

Average age of Female ⇒ 7x

Sum of ages of Male = 5x × 60= 300x

Sum of ages of Female = 7x × 40= 280x Sum of ages of Total Employees

100= 29

300x + 280x = 2900

580x = 2900

x = 5

Average age of females

= 7x = 7 × 5 = 35 years

S8. Ans.(b)

Sol. Total no. of people per week= 40 × 7= 280

Let n be no. of holidays

(7 – n) × (40 + 16) = 280

(7 – n) × 56 = 280

7 – n = 5

n = 2

No. of holidays = 2

S9. Ans.(d)

Sol. Age of 4 Males = 4 × 42= 168

Age of 7 females = 7 × 20= 140

Age of whole family = 168 + 140= 308

Average age of family = 308/11= 28 years

Age of two persons who left = 13 × 2 = 26 years

Age of 9 members in family = 308 – 26= 282

Age of 12 member in family after having 3 new members

= 282 + 11 + 15 + 28 = 336

Average age of New family

= 336/12 = 28 years

Average age of the family increases by 0 years

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S10. Ans.(b)

Sol. Let Numbers are

a – 5, a – 3, a – 1, a + 1, a + 3, a + 5

Average of these odd numbers

=a − 5 + a − 3 + a − 1 + a + 1 + a + 3 + a + 5

6=

6𝑎

6= 𝑎

ATQ

(a – 5)² + (a + 5)² = 178

a² + 25 – 10a + a² + 25 + 10a = 178

2a² + 50 = 178

2a² = 128

a² = 64

a = 8

S11. Ans.(b)

Sol. Let length of pencil x & length of broken parts is a & b 𝑥

𝑎=

𝑎

𝑏

x = a + b

𝑎 + 𝑏

𝑎=

𝑎

𝑏

ab + b² = a²

a² – b² – ab = 0 …(i)

Let b = 1

a : b = a : 1

Putting b = 1 in (i)

a² – 1 – a = 0

a² – a – 1 = 0

Using quadratic

𝑎 =−𝑏 ± √𝑏2 − 4𝑎𝑐

2𝑎

𝑎 =1 + √1 + 4

2

𝑎 =1 + √5

2

𝑎 ∶ 𝑏 = 1 + √5

2∶ 1

= 1 + √5 ∶ 2

x = a + b = 2 + 1 + √5

= 3 + √5

b : x = 2 : 3 + √5

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S12. Ans.(b)

Sol.

⇒ 2x, 2x, 3x, 4x

Total marks ⇒ 2x + 2x + 3x + 4x

⇒ 11x

Maximum marks in each subject are equal

∴ Aggregate % = 11

4𝑥

ATQ, 11

4𝑥 = 55

x = 20

History → 40

Sociology → 40

Geography → 60

Philosophy → 80

Hence in two subjects he scored more than equal to 60%

S13. Ans.(d)

Sol. Income → Anil : Mukesh → 2 : 3

Anil → 2x

Mukesh → 3x

Let savings of Anil → K

Then Expenditure of M → K

Expenditure of A = 2x – K

2x – k + k = 800

2x = 8000

x = 4000

Total Income of A + B

= 5x = 20000

Total saving of A & B = 20000 – 8000

= 12000 Rs.

S14. Ans.(b)

Sol. Profit of Hutch

Profit of Essar=

time × amount of H

time × amount of E

6

17=

5 × 𝑘

12 × 1275

k = 1080

H :So 1:1

S: Geo 2 :3

History : Pil 1: 2

H :S: G : P 2 : 2 :3: 4

→

→

→

→

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S15. Ans.(b)

Sol. Concentration of Petrol

Total P → 1 + 1.8 + 0.8 → 3.6L

Total K = (2 + 3 + 1) – 3.6

= 6 – 3.6 = 2.4

Ratio = 3.6 : 2.4=3 : 2

S16. Ans.(b)

Sol. Stressed Milk : Water

1 → x : 2

3𝑥

3 : 2

Water → 2

5

2nd → 100 : 40

5 : 2

Water ⇒ 2

7

S17. Ans.(a)

Sol. Efficiency of 6 K Pumps → 1

7

Efficiency of 1 K Pumps → 1

7 × 6=

1

42

Efficiency of 2 Usha pumps = 1

18

Efficiency of 1 usha pump = 1

36

Ratio = 1

42∶

1

36

= 6 : 7

1 3 4, ,

2 5 5

2L 3L 1L

P 1 1.8 0.8

→

→ → →

2 2:

5 7

1

3

1 2 2 1:

3 7 5 3

(5 : 7)

− −

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S18. Ans.(b)

Sol. Cello : Rotomac

2000 → 3 : 5

Cello → 3x

Rotomac → 5x

2005 → Cello → 3x × 3 = 9x

Rotomac → 5x + 100 9𝑥

5𝑥 + 100=

4

5

45x = 20x + 400

25x = 400

x = 16

Rotomac = 5 × 16= 80 Rs.

S19. Ans.(a)

Sol. D : S

M₁ → 7 : 3

M₂ → 5 : 4

Resultant → 2 : 1

S20. Ans.(c)

Sol.

8 : 2

3 : 2

10r → 1.5

1r → 0.15

Weigh of grapes crushed = (8 – 3) r

= 5r

= 5 × 0.15

= 0.75 kg

1 2Dew in M Dew in M

7 5

10 9

2

3

2 5 7 2:

3 9 10 3

1 1:

9 30

10 : 3

− −

Water : Pulp

Fresh 4 : 1 2

Crushed 3 : 2

→

→

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S21. Ans.(b)

Sol. 1500

𝑥=

1500

𝑥 + 250+

1

2

3000x + 3000 × 250 = 3000x + x² + 250x

x² + 250x – 3000 × 250 = 0

x² + 1000x – 750x – 3000 × 250 = 0

x = 750 km/hr

S22. Ans.(c)

Sol. Speed Ratio

5 : 7

Time Ratio (∝1

𝑠𝑝𝑒𝑒𝑑) ⇒ 7 : 5

(7 – 5)r → 30 + 6

2r = 36 min

1r → 18 min

7r → 126 minute

Distance = 5 m/min × 126 m

= 630 meters

S23. Ans.(a)

Sol. Let speed of car be x

(𝑥 − 2) =0.6

6× 60

(x – 2) = 6

X = 8 km/hr

S24. Ans.(b)

Sol. Distance travelled by A in 1 hr = 20 km

Remaining distance = 110 – 20 = 90

Time = 90

20 + 25

=90

45

= 2 hours

They will meet at= 8 am + 2 h

= 10 a.m.

S25. Ans.(b)

Sol. Time taken to catch the thief = 200

1×5/18

= 40 × 18 sec

= 40×18

60

= 12 minutes

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S26. Ans.(d) Sol.

Since ABCD is a cyclic Quadrilateral ∴ ∠A + ∠C = 180° ..(i) & ∠B + ∠D = 180° …(ii) But ABCD is a parallelogram ∴ ∠A + ∠D = 180° …(iii) & ∠B + ∠C = 180° …(iv) Thus from (i), (ii), (iii) & (iv) ∠A = ∠B = ∠C = ∠D = 90° ∠B = 90° S27. Ans.(b) Sol.

Let ABCD be is a square 4 quarter circles with radius 2 cm Comprises a complete circle of radius 2 cm Remaining portion. = Area of square – Area of circle = (4)2 − πr² = 16 - π (2)² = (16 – 4π ) cm² S28. Ans.(b) Sol.

Area of ABCD =

1

2(8 + 𝐵𝐶)ℎ

1

2(8 + 𝐵𝐶)ℎ = 2√15 +

1

2𝐵𝐶 × ℎ

⇒ ℎ =√15

2

𝐵𝐶

2= √16 −

15

4

⇒ BC = 7 cm

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S29. Ans.(a)

Sol.

PO = r (radius)

PQ = QR = a (say)

‘r’ is radius of circumcircle of ∆PQR

∴r =a

√3

a = √3r

∵ M will be midpoint of QR and PM ⊥ QR

MS = 2r – PM

MS = 2r −√3

2a

MS = 2r −3

2r =

r

2 and MR =

a

2=

√3

2r = QM

QS = √MQ2 + MS2 = r

RS = √MR2 + MS2 = r

Perimeter of PQSR = PQ + QS + SR + PR = r√3 + r√3 + r + r

= 2r(1 + √3)

S30. Ans.(c)

Sol.

∠PAC = 180° - (75° + 45°)

∠PAC = 180° - 120°

= 60°

By alternate segment theorem,

∠PAC = ∠ABC = 60°

∠ABC = 60°