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Simple Interest

1. What is the SI onRs.2500/- at the rate of 12% per annum for 8 years? Ans :2400

Difficulty Level : Easy Yes Moderately easy Difficult

Basic Formula:

Simple Interest is denoted by SI

S.I = 100PNR

P – Principal amount, N- Number of years, R – Rate of Interest

Answer with Explanation:

Given P = 2500, N = 8 Years, R = 12%

There fore S.I = 100PNR

S.I = 100

8122500 XX

S.I = 2400

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2. What is the SI on Rs.7500/- at the rate of 10% per annum for 5 years? Ans 3750


Basic Formula:


S.I = 100PNR



Given P = 7500, N = 5 Years, R = 10%

There fore S.I = 100PNR

S.I = 100

5107500 XX

= 75 X 5 X 10

S.I = 3750




3. A man borrowed rs.5000/- at the rate of 8% SI and to clear the debt after 6 years, how much he has to return : Ans 7400

Difficulty Level : Easy Moderately easy Yes Difficult

Basic Formula:


S.I = 100PNR



Given P = 5000, N = 6 Years, R = 8%

There fore S.I = PNR / 100

S.I = 100

685000 XX

= 50 X 6 X 8

S.I = 2400

Total repayment = S.I + Principal amount

Answer = 2400 + 5000 = Rs 7400




4. A man borrowed Rs.8000 at the rate of 12% SI, and lent the same sum to another person at the rate of 15% what will be the gain after 7 year ? ans 1680

Difficulty Level : Easy Moderately easy Difficult Yes

Basic Formula:

Answer with Explanation:Given :

A man borrowed at 12%

He lent the same sume to another person at 15%

Therefore his gain is 15 – 12 =3% for 1 year

Given N = 7 years and P = Rs. 8000

First we are calculating for Rs. 100

For 100 = 3 X 7 = 21

For 1000 = 210

For 8000 = 1680

Therefore his gain = Rs. 1680/-




5. Mr.A borrowed Rs.12000/- at the rate of 10% and lent the same amount to Mr.B. at the rate of 13% what will be gain of A, after 5 years. Ans 1800


Basic Formula:

S.I = 100PNR



Given P = 12000, N = 5 years,

(i) R = 10%, (ii) R = 13%

Case (i)

S.I = 100PNR

= 100

10512000 XX

= Rs. 6000/-

Case (ii):

S.I = 100PNR

= 100

13512000 XX

= Rs. 7800/-

Difference = Rs. 7800 – Rs. 6000

= Rs. 1800/-

Therefore Gain = Rs. 1800/-

Note : Problems 4 and 5 both are same type. So either you follow the method given in 4th problem (or) 5th problem.




6. In what time, we can get Rs.1200/- as SI on Rs.5000/- at the rate of 8%? Ans 3


Basic Formula:

S.I = 100PNR


Time = Number of years (N)


Given :

S.I. = Rs. 1200/-

P = Rs. 5000/-

R = 8%

To find time (Number of years (N) )

1200 =100

85000XNX

1200 = 400 N

N = 1200/400

N = 3

Therefore N = 3 years




7. In what time RS.6000/- give RS.2880/-as SI at the rate of 12%? Ans 4

Difficulty Level : Easy Moderately easy Difficult

Basic Formula:

S.I = 100PNR


Time = Number of years (N)


Given :

S.I. = Rs. 2800/-

P = Rs. 6000/-

R = 12%

To find time (Number of years (N) )

2800 =100

126000XNX

2800 = 720 N

N = 2800/720

N = 4

Therefore N = 4 years




8. Mr. Manager took a loan of Rs.25000/- for 5years at SI. If the interest paid were Rs.12500/- what is the rate of interest per annum? Ans10%


Basic Formula:

S.I = 100PNR

Interest = Simple Interest


Given :

P = Rs. 25000/-

S.I = Rs. 12500/-

N = 5 Years

To find R

12500 = 100

525000 XRX

R = 12500 / 1250

= 10%

Therefore the Rate of Interest = 10%




9. Mr. Thiru borrowed Rs.50000/- for 3 years at SI. If the interest paid was Rs.18000/- find the rate of SI? Ans 12%


Basic Formula:

S.I = 100PNR

Interest = Simple Interest

Answer with Explanation:Given :

P = Rs. 50000/-

S.I = Rs. 18000/-

N = 3 Years

To find R

12500 = 100

350000 XRX

R = 18000 / 1500

= 180 / 15

= 12

Therefore the Rate of Interest = 12 %




10. Mr.Raj got a loan at 11% p.a. SI after 5 years he returned the principal along with interest. If he returns in all RS.12400/- what is the principal amount Ans:8000


Basic Formula:

S.I = 100PNR


Given R = 11%, N = 5 years, S.I + P = Rs.12400/-

To find P,

We know that S.I = 100PNR

S.I + P = 100PNR

+ P

(ie) 12400 =100

115XPX + P

12400 =10055P

+P

12400 = P {10055

+1}

= P {100155

}

P = 12400 X 100/155

P = Rs. 8000/-




11. Mr.Krishnan received a loan at 13% p.a. SI. After 4 years he returned the principal and interest. If he returned Rs.9120/- what will be principal amount ? Ans:6000


Basic Formula:

Note : Problems 10 and 11 are of same type. So you can follow either the following method or 10th problem method.


Given

R = 13%, N = 4 years, S.I + P = Rs.9120/-

Short cut method:

First we are calculating for Rs. 100/-

100 = 13 X 4 (R X N) for number of years

100 = 152 (Amount =100 and the Interest = 52)

? = 9120

P = 100 X 9120 / 152

P = 6000

Principal Amount = Rs.6000/-




12. If Rs.700/- amount to Rs.16800/- in 5 years SI. If the rate of interest is increased by 5%. It would amount to how much? Answer : Rs.10,150


Basic Formula:

Given rate of interest is increased, so we add the given amount and the calculated amount


P = Rs. 700, N= 5 years, Increased rate of interest R = 5%

Short cut method:

First we are calculating it for 100 rupees

100 : 5 X 5 = 25 (NXR)

700 : 25 X 7 = 175

Given amount + S,I = Rs. 16800 + 175 = 16975

Therefore the amount = Rs. 16975/-




13. If Rs.12000/- amount to Rs.16800/- in 5 years If the rate of interest is increased by 2%. What would be the amount? Answer : Rs.18,000


Basic Formula:

Given rate of interest is increased, so we add the given amount and the calculated amount

Answer with Explanation:P = Rs. 12000, N= 5 years, Increased rate of interest R = 2%

Short cut method:


100 : 5 X 2 = 10 (NXR)

(ie) for 100 rupees the interest is Rs. 10100 = 101000 = 10010000 = 10002000 = 200

There for 12000 = 1000 + 200 = 1200Given amount + S,I = Rs. 16800 + 1200 = 18000





14. If Rs.10,000/- amount to Rs.14000/- in 5 years If the rate of interest is reduced by 3%. What would be amount? Answer : Rs.12,500


Basic Formula:

Given rate of interest is reduced, so we subtract the given amount and the calculated amount

Answer with Explanation:P = Rs. 10000, N= 5 years, Increased rate of interest R = 3%

Short cut method:


100 : 5 X 3 = 15 (NXR)

(ie) for 100 rupees the interest is Rs. 15100 = 151000 = 15010000 = 1500

Given amount + S,I = Rs. 14000 - 1500 = 12500





15. A principal amount to RS.8880/- in 4 years and Rs.9600/- in 5 years what is the rate of interest?Ans 12%


Basic Formula:

S.I = 100PNR

Amount = Principal + S.I


S,I for one Year = Rs.720 (9600 – 8880)

S.I for 4 years = Rs.2880

Principal = Amount – S.I

= 8880 – 2880

= 6000

R = PNSIX100

= 46000

1002880X

X

= 288/6X 4

= 48/4 = 12

Therefore R = 12%.




16. A certain sum of money lent out of SI amount to Rs.8000/- 6 years Rs.9000/- in 8 Years. Find the sum and the rate of interest? Answer 10%


Basic Formula:

S.I = 100PNR

Amount = Principal + S.I

Answer with Explanation:Given:

S.I for 2 years = 1000 (9000-8000)

(8-6)

S.I. for 1 year = 500

S.I for 6 years = 3000

P = Amount – S.I

= 8000-3000

P = 5000

R =65000

3000100X

X

= 100/10

R = 10%




17. A certain sum give RS.9000/- as SI for 8 years at the rate of 12% what will be the

SI on the same sum for 12 years at the rate of 8% ?

Answer: 9000


Basic Formula:

S.I = 100PNR


We split the given problem into 2 parts

Part (i)

Given S.I = 9000, N = 8, R = 12

∴ S.I. = 100

128XPX

9000 = 100

128XPX ------------------(1)

Part (ii)

Given N=2, R = 8

∴ S.I. = 100

812XPX ------------------(2)

From (1) and (2), S.I = Rs. 9000/-

Shortcut method:

Number of years in Part (i) = Rate of interest in Part (ii)

Rate of interest is part (i) = Number of years in part (ii)

⇒ S.I. = Rs. 9000/-




18. A Principal amount give Rs.12000/- as SI for 7 years at the rate of 11% to get the same amount of interest of 11 years, what will be the rate of interest

Ans.: 7%


Basic Formula:

S.I = 100PNR

Results:

Number of years in Part (i) = Rate of interest in Part (ii)

Rate of interest is part (i) = Number of years in part (ii)



Part (i)

Given P = 12000, N = 7, R = 11

Part (ii)

Given P = 12000, N = 11,

Using the results(in the formula),

R = 7%




19. Mr.A. give Rs.1500/- to Mr.X for 4 years and Rs.2500/- to mr.Y. for 8 years. If the rate of intest is the same and Mr.A received Rs.2080/- from both Mr.X and mr.Y what is the rate of SI ?

ans: 8%


Basic Formula:

S.I = 100PNR


Given :

For X, P = 1500, N = A

For Y, P = 2500, N= 8

S.I = Rs. 2080 ( For X and Y)

∴ 100

41500 XRX +

10081500 XRX

= 2080

60R + 200R = 2080

260R = 2080

R = 2080 / 260

R = 8%

∴ Rate of interest of SI = 8%




20. Ms.Varshini gave Rs.30000/- to Mr.Suresh for 5 years and Rs.20000/- to Mr.Vijay for 2 ½ years. If the rate of interests is the same and she received Rs.14000//- as SI from both. What is the rate of interest?

Ans: 7%


Basic Formula:

S.I = 100PNR


Given :

X : Ms.Varshini, Y: Mr.Vijay

For X, P = Rs.30000/-, N=5

For Y, P= Rs.20000/-, N= 2 ½

S.I = Rs. 14,000 (For X and Y)

∴ 100

530000 XRX +

1002

1220000 XRX = 14000

1500R +500R = 14000

2000 R = 14000

2R = 14

R = 7

∴ Rate of interest = 7%




21. What would be the SI on Rs.48000/- for 4 years at the rate of 6 ¼% :Ans 12,000


Basic Formula:

S.I = 100PNR

Answer with Explanation:Given:

P = Rs. 48000/-, N = 4, R = 6 ¼

S.I = 100

416448000 XX

=100

425448000 XX

= 480 X 25

= 12000

∴ S.I = 12,000




22 What will be the SI on Rs.60000/- for 3 years at the rate of 8 1/3% Ans 15,000


Basic Formula:

S.I = 100PNR


Given,

P = Rs. 60,000, N=3, R = 8 1/3

S.I = 100PNR

S.I = 100

318360000 XX

=100

325360000 XX

= 600 X 25 = 15,000

∴ S.I = Rs. 15,000/-






Basic Formula:

S.I = 100PNR


Given,

P = Rs. 75,000, N=3, R = 16 2/3

S.I = 100PNR

S.I = 100

3216375000 XX

=100

350375000 XX

= 750 X 50 = 37500

∴ S.I = Rs. 37500/-






Basic Formula:

S.I = 100PNR


Given,

P = Rs.25,000, N=3, R = 33 1/3

S.I = 100PNR

S.I = 100

3133325000 XX

=100

3100325000 XX

=100

10025000X= 25,000

∴ S.I = Rs. 25,000/-




25 A sum of money becomes double in 10 years. What is the rate of interests Ans:10%


Basic Formula:

S.I = 100PNR

Answer with Explanation:Given : N = 10

Let the sum be x, Then S.I = x

Given a sum becomes double

⇒ S.I = Sum

S.I = 100PNR becomes

X = 10010XRxX

100x = 10x X R

X = 10

Rate of Interest = 10%




26. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He

immediately lends it to another person at 6 1/4% p.a. for 2 years. Find his gain in

the transaction per year.

Rs.112.50 Rs.125 Rs.150 Rs.167.50


Basic Formula:

S.I = 100PNR

Answer with Explanation


Part (i)

Given P = Rs. 5000, N=2, R = 4%

S.I = 100

425000 XX = 100X 4

S.I = 400

Part (ii)

Given P = Rs. 5000, N=2, R = 6 ¼ %

S.I = 100

41625000 XX =

1004

2525000 XX = 100

255000X = 25 X 25

S.I = 625

Gain = 625 -400 = 225 for 2 years

∴ Gain for one year = Rs. 112.50




27. How much time will it take for an amount of Rs.450 to yield Rs.81 as interest at 4.5% p.a. of simple interest? 3.5 years 4 years 4.5 years 5 years


Basic Formula:

S.I = 100PNR

Time = Number of years


Given P = Rs. 450, S.I=Rs. 81/-, R = 4.5%


81 = 100

5.4450XNX

81 = 2025N / 100

8100 = 2025N

N = 8100 / 2025

N = 4

∴ Number of Years = 4




28. What is the present worth of Rs.132 due to 2 years at 5% simple interest per

annum?

Rs.112 Rs.118.80 Rs.120 Rs.20,000


Basic Formula:

S.I = 100PNR


Let the present worth be x ( ie Principal = x)

Then S.I = Rs (132 – x)

Given N = 2, R = 5


132-x = 100

52XxX

132-x = 10x / 100

132-x = x/10 ⇒ 1320 – 10x = x

11x = 1320

X = 1320 / 11 = 120

∴ Present worth = Rs. 120/-




29. In how many years, Rs.150 will produce the same interest at 8% as Rs.800

produce in 3 years at 4 1/2%?

6 8 9 12


Basic Formula:

S.I = 100PNR

Answer with Explanation We split the given problem into 2 parts

Part (i)

Given P = 150, R = 8

∴ S.I. = 100

8150XNX------------------(1)

Part (ii)

Given P = Rs. 800/- N=3, R = 4 ½

∴ S.I. = 100

2143800 XX

= 100

293800 XX

=100

93400 XX------------------(2)

From (1) and (2),

1008150XNX

=100

93400 XX ⇒2

83XNX= 4 X 3 X9

3 X N X 4 = 4 X 3 X 9⇒ N = 9

∴ Number of Years = 9




30. Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs.8160, how much money did he borrow?Rs.8000 Rs.10, 000 Rs.12, 000 Rs.1500


Basic Formula:

S.I = 100PNR



Part (i) R = 6, N = 3

Part (ii) R = 9, N=3

Part (iii) R = 13, N = 11-8 = 3

S.I = Rs. 8160/-

∴

10036XPX

+

10059XPX

+

100313XPX

= 8160

10018P

+ 10045P

+ 10039P

= 8160

100394518 PPP ++

= 8160 ⇒ 100

102P = 8160

102 P = 816000

P = 102

816000 = 8000

P = Rs. 8000/-




31. What will be the difference between simple and compound interest at 10% per

annum on a sum of Rs.1000 after 4 years?

Rs.31 Rs.64.10 Rs.40.40 Rs.40.45 Difficulty Level : Easy Moderately easy Difficult

Basic Formula:

S.I = 100PNR

C.I = P

+

1001 R N


(i) S.I = 100

4101000 XX

S.I = 100 X4

S.I = 400

(ii) C.I = 1000

+

100101 4 - 1000

=1000

100110 4 – 1000 = 1000

1011 4 - 1000

=1000 X 1011

X1011

X 1011

X 1011

- 1000

=1464.1 – 1000 = 464.1

C.I. = 464.1

Difference = C.I – S.I = 464.1 – 400 = 64.10

Difference = 64.10




32. A sum of money at simple interest amounts to Rs.815 in 3 years and to Rs.854

in 4 years. The sum is:

Rs.650 Rs.690 Rs.698 Rs.700


Basic Formula:

Answer with Explanation Given:

Amount at SI for 3 years = Rs. 815

Amount at SI for 4 years = Rs. 854

∴ SI for 1 year = (854 – 815 = Rs. 39/-

SI for 3 years = 39 X 3 = 117

∴ Amount = Rs (815-117) = 698

Amount = Rs. 698/-




33. A sum of money trebles itself in 15 years 6 months. In how many years would it double itself?6 years 3 months 7 years 9 months 8 years 3 months 9 years 6 months


Basic Formula:

S.I = 100PNR

Amount = Sum + S.I


Let sum = x, Then SI = 2x

S.I = 100PNR

becomes [Sum + SI = x +2x = 3x]

2x = 100

2/31xXRX[ N = 15 ½ = 31/2]

200 = 31/2 RR = 400/31

Now sum = x, S.I =x [Sum + SI = 2x = Double the amount]

X = 100

31/400xXNX

100x = 31

400xN

31 = 4N ⇒ N = 31/4 ⇒ 7 ¾∴ N = 7 years 9 months




34. In how much time would the simple interest on a certain sum be 0.125 times

the principal at 10% per annum?

1 1/4 years 1 3/4 years 2 1/4 years 2 3/4 years


Basic Formula:

S.I = 100PNR

R = PN

SIX100


Let Principal = x

Given simple interest = .125 time the principal

(ie) SI = .125x

= 1000

1000125. X x = 125x/1000

S.I = 1/8x

Given R = 10%

S.I =100PNR becomes

1 x /8 = 100

10xXNX ⇒ 1 x /8 = Nx/10

1/8 = N/10 ⇒ N = 10/8 = 5/4 years

N = 1 ¼ years∴ Time = 1 ¼ years




35. Simple interest on a certain amount is 9/16 of the principal. If the numbers

representing the rate of interest in percent and time in years he equal, then time, for

which the principal is lent out, is:

5 1/2 years 6 1/2 years 7 years 7 1/2 years


Basic Formula:

S.I = 100PNR


Given Simple interest = 9/16 of the principal

(ie) S.I = 169 P ----------------------(1)

Given Rate of interest = Time in Years

(ie) R = N ------------------(2)

∴ 100PNR = S.I becomes

100PXNXN =

169 P [from (1) and (2)]

100

2N = 169 ⇒ N2 =

16900

N = 4

30 = 7.5

N = 7 ½ Years




36. The difference between compound interest and simple interest on an amount of Rs.15, 000 for 2 years is Rs.96. What is the rate of interest per annum?8 10 12 None of these


Basic Formula:

S.I = 100PNR

C.I = P

+

1001 R N – P

(a+ b)2 = a2 + 2ab + b2


Given P = Rs.15000, N = 2

C.I – S.I = Rs. 96/-

∴

−

+ 15000

100115000

2R -

100215000XRX

= 96

−

−+ 150001

10000)100(15000

2R -

100215000XRX

= 96

15000

−+ 1

10000)100( 2R

- 15000 X1002R

= 96

15000

−−+

10021

10000)100( 2 RR

= 96

15000

−−++10000

2001000020010000 2 RRR = 96

1015 2R = 96 ⇒ R2 =

151096X ⇒ R2 = 64 , R = 8





37. A lent Rs.5000 to B for 2 years and Rs.3000 to C for 4 years on simple interest

at the same rate of interest and received Rs.2200 in all from both of them as

interest. The rate of interest per annum is:

5% 7% 8% 10%


Basic Formula:

S.I = 100PNR

Answer with Explanation We split the given problem into 2 parts

Given

Part (i) P=Rs.5000, N = 2

Part (ii) P = Rs. 3000/-, N = 4

S.I = Rs. 2200/-

∴ 2200 = 100

25000 XRX +

10043000 XRX

2200 = 100R +120R

2200 = 220R

R = 2200/220

R = 10





38. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 Years?Answer : 2:3


Basic Formula:

Answer with Explanation Let P = Principal, R- Rate of interest

Case (i)

N = 6

Case (ii)

N = 9

∴ Ratio = 100

9100

6

XRPX

XRPX

= 6PR / 9PR

6/9 = 2: 3




39. At what rate per cent per annum will be simple interest on a sum of money be 2/5 of the amount in 10 years?Answer : 4%


Basic Formula:

S.I = 100PNR

R = PNSIX100


Given

N = 10

Let Sum = x (Principal amount)

S.I = 2x / 5

R = PNSIX100

becomes

R = 10

1005/2xX

Xx

R = 10202

xXxX ⇒ 2 X 2 = 4

R = 4




40. A man borrowed certain amount for 6 years at the rate of 5% and paid a SI of Rs. 1230. What is the principal amount? Answer : Rs. 4100


Basic Formula:

S.I = 100PNR


Given

N = 6, R = 5, S.I = 1230

S.I = 100PNR

becomes

1230 = 100

56XPX

1230 = 6P/20 ⇒ 3P/10

3P = 12300

P = 4100

Amount = Rs. 4100/-




41. Rs. 2,500 earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?Answer : 350


Basic Formula:

S.I = 100PNR


Given

P = Rs. 2500/-, N = 7, R = 2,

S.I = 100PNR

becomes

= 100

272500 XX

= 25 X 7 X 2 = 350

More interest is Rs. 350/-




42. A sum of money becomes 5/4 of itself in 5 years at a certain rate of interest. What is the rate of interest?Answer : 5%


Basic Formula:

S.I = 100PNR

Sum = Principal

R = PNSIX100

Amount = Principal +SI


Let sum = x

Then Amount = 5x/4

S.I = Amount – Sum

= 5x/4 –x = 1x/4

R = 5

10041

xX

xX

R = 25/5

R = 5%




43. At what rate percent per annum will a sum of money double in 16 years ?Answer : 6.25%


Basic Formula:

S.I = 100PNR



Given

Let Sum = x

Then SI =x, time = 16 years { ( SI + Sum = double the amount) x+x = 2x}

x = 10016XRxX

16100

xXxX

= R

R = 100/16 = 50/8 = 25/4

R = 12.5/2

R = 6.25%




44. The simple interest on a sum of money is 4/9 of the principal. Find the rate percent and time, if both are numerically equal.Answer: 6 Years 8 Months


Basic Formula:

S.I = 100PNR


Given

(i) S.I = 4P/5

(ii) Rate percent = Time

(ie ) R = N

S.I = 100PNR

becomes

94

P = 100PNN

94

= 100

2N

9N2 = 400

N2 = 400/9 ⇒ 20/3 = N

N = 6 years 2/3 years

N = 6 years 8 months




45. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs.5400 interest only. The principal amount borrowed by him was:Answer : 15,000


Basic Formula:

S.I = 100PNR

Answer with Explanation Given

S.I = Rs. 5400/-, N = 3, r=12

S.I = 100PNR

becomes

5400 =100

123XPX

5400 =50

18P

18P = 270000

P = 18

270000 = 15,000

Principal amount = Rs. 15,000/-




46. If the sum of money double in 5 years. It will become 4 times in ?Answer : 15


Basic Formula:

S.I = 100PNR



Given

Let Sum = x, Then SI =x,

S.I = 100PNR

becomes

x = 100

5XRxX

R = xx

5100 ⇒ R = 20% ( SI + Sum = 3x +x = 4x)

Now, Sum = x, S.I = 3x, R = 20%

S.I = 100PNR

becomes

3x = 100

20xXNX ⇒ 3 = 102N

2N = 30 ⇒ N = 15


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