Simple And Compound Interest Solved Questions

Simple And Compound Interest Solved Questions

1.Mr. Hamilton invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B? 

a) Rs. 6400

b) Rs. 6500
c) Rs. 7200
d) Rs. 7500
e) None of these
1. Option A

Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 ⎯ x)

Then, [ x  × 14  × 2  / 100] ÷ [{(13,900 – x) × 11  × 2 } / 100] = 3508

28x ⎯ 22x = 350800 ⎯ (13900 ×  22)

6x = 45000

x = 7500

So, sum invested in Scheme B = Rs. (13900 ⎯ 7500) = Rs.6400

2.How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

a) 3.5 years
b) 4 years
c) 4.5 years
d) 5 years
e) None of these

2.  Option B
Time = [100 × 81 / 450 × 4.5  ] years = 4 years

3.A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

a) 3%

b) 4%

c) 5%
d) 6%

e) None of these

3. Option D

S.I. = Rs. (15500 ⎯ 12500) = Rs.3000

Rate = [ 100 × 3000 / 12500 × 4 ]% = 6%

4.An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

a) 10%

b) 10.25%

c) 10.5%
d) Data inadequate

e) None of these

4. Option B

Let the sum be Rs.100. Then,

S.I. for first 6 months = Rs. [100 × 10 × 1  / 100 × 2] = Rs.5

S.I. for last 6 months = Rs. [105 × 10 × 1  / 100 × 2] = Rs.5.25

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs.110.25

So, effective rate = (110.25 ⎯ 100) = 10.25%

5.Aastha lent Rs. 5000 to Bahubali for 2 years and Rs. 3000 to Chinky 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:

a) 5%

b) 7%

c) 7 1/8%
d) 10%

e) None of these

5. Option D

Let the rate be R% p.a.

Then, [ 500 × R × 2  / 100 ] + [300 × R × 4  / 100] = 2200

100R + 120R = 2200

R = [2200  / 220] = 10

So, rate = 10%

6.Aman took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

a) Rs. 2000

b) Rs. 10,000

c) Rs. 15,000
d) Rs. 20,000

e) None of these

6. Option C

Principal = Rs. [ 100 × 5400  / 12 × 3] = Rs.15000

7.What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 9 years?

a) 1 : 3

b) 1 : 4

c) 2 : 3
d) Data inadequate

e) None of these

7.Option C

Let the principal be P and rate of interest be R%.

So, required ratio = [P × R × 6 / 100] / [P × R × 9 / 100]   = 6PR / 9PR   = 6 / 9 = 2 : 3

8.Akshay borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 ¼ pa for 2 years. Find his gain in the transaction per year.

a) Rs. 112.50

b) Rs. 125

c) Rs. 150
d) Rs. 150

e) Rs. 167.50

8. Option A

Gain in 2 years = Rs. [(5000 × 25 / 4 × 2 / 100  ) ⎯ (5000 × 4 × 2 / 100 )]

= Rs. (625 ⎯ 400)

= Rs.225

So, gain in 1 year = Rs. [225  / 2] = Rs.112.50

9.On a sum of money, the simple interest for 2 years is Rs.660, while the compound interest is Rs.696.30, the rate of interest being the same in both the cases. The rate of interest is :

a) 10%

b) 10.5%

c) 12%
d) Data inadequate

e) None of these

9. Option E

Difference in C.I. and S.I. for 2 years – Rs. (696.30 ⎯ 660) = Rs.36.30

S.I. for one year = Rs.330

10.Mr.Devilal Singh invested an amount of Rs.13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs.3508,  what was the amount invested in Scheme  B?

a) Rs.6400

b) Rs.6500

c) Rs.7200
d) Rs.7500

e) None of these

10. Option A

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 ⎯ x)

Then, [x × 14 × 2  / 100 ] + [(13,900 – x) × 11 × 2  / 100] = Rs.3508

28x ⎯ 22x = 350800 ⎯ (13900 × 22 )

6x = 45000

x = 7500

So, sum invested in Scheme B = Rs. (13900 ⎯ 7500) = Rs.6400

11.What should be the least number of years in which the simple interest on Rs.2600 at 6⅔%  will be an exact number of rupees?

a) 2

b) 3

c) 4
d) 5

e) None of these

11. Option B

S.I. = Rs. [2600 × 20 / 3 × 1 / 100 × T] = Rs.[  520 / 3 × T]

Which is an exact number of rupees when T = 3

12.An amount of Rs.1,00,000 is invested in two types of shares. The first yields an interest of 9%  p.a. and the second, 11% p.a. If the total interest at the end of one year is 9¾%, then the  amount invested in each share was :

a) Rs.52,500, Rs.47,500

b) Rs.62,500, Rs.37,500
c) Rs.72,500, Rs.27,500

d) Rs.82,500, Rs.17.500

e) None of these

12. Option B

Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 ⎯ x)

Then, [x × 9 × 1  / 100  ]  + [ (100000 – x) × 11× 1 / 100  ] = [100000 × 39 / 4 × 1 / 100  ]

9x + 1100000 – 11x / 100 =  39000 / 4 = 9750

2x = (1100000 ⎯ 975000) = 125000

x = 62500

Sum invested at 9% = Rs.62500

Sum invested at 11% = Rs. (100000 ⎯ 62500) = Rs.37500

13.If the simple interest on a certain sum for 15 months at 7½% per annum exceeds the simple interest on the same sum for 8 months at  12½% per annum by Rs.32.50, then  the sum (in Rs.) is :

a) Rs.3000

b) Rs.3060

c) Rs.3120
d) Rs.3250

e) None of these

13. Option C

Let the sum be Rs. x. Then, [x × 15 / 2   × 5 / 4 × 1 / 100  ] ⎯ [x × 25 / 2 × 2 / 3   × 1 / 100  ]

=   32.50

75x / 8  ⎯ 25x / 3  = 3250

25x = (3250 × 24)

x = [3250 × 24 / 25] = 3120

14.A sum of money trebles itself in 15 years 6 months. In how many years would it double itself?

a) 6 years 3 months

b) 7 years 9 months

c) 8 years 3 months
d) 9 years 6 months

e) None of these

14. Option B

Let sum = x. Then, S.I. = 2x, Time = 15 (1/2) years =  31 / 2 years

So, rate = [ 100 × 2x / x  × (31/2)]% = 400 / 31%

Now, sum = x, S.I. = x, Rate = 400 / 31%

So, time = 100 × x / x  × (400/31) = 31 / 4  years = 7 years 9 months

15.Rambo took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If he paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

a) 3.6

b) 6

c) 18
d) Data inadequate

e) None of these

15. Option B

Let rate = R% and time = R years

Then, [1200 × R  × R / 100] = 432

12 r2 = 432

R2 = 36

R = 6

16. A sum of money four folds itself in 24 years o compound interest. With the same rate per cent per annum the amount becomes sixteen times itself in.
(a) 48 years
(b) 72 years
(c) 24 years
(d) 96 years

16. Option a

(a) 48 years
Hint: If a certain amount at compound interest become K times in n years, then the sane amount becomes k times in n* r years

17. A sum of money doubles itself in 10 years. A compound interest is charged on it at x% p.a. with the same rate p.a. it will four-fold itself in
(a) 15 years
(b) 20 years
(c) 40 years
(d) 30 years

17. Option b

 (b) 20years

18. At what rate per cent per annum will a sum of Rs 6250 amount to Rs 7840 in 2 years, interest is compounded annually?
(a) 9%
(b) 10%
(c) 10%
(d) 11%

18. Option d

(d) 12 %
Hint: 

19. A sum of money amount to RS 14,520 in 2 years and to Rs 15,972 in 3 Years reckoning compound interest at the rate of
(a) 5%
(b) 10%
(c) 15%
(d) 20%

19. Option b

 (b) 10%
Hint:

20. The difference between compound interest and simple interest on a certain sum at 6.25% p.a. for 2 years is Rs 70.31 What is sum?
(a) 18000 approx.
(b) 16000 approx.
(c) 14000 approx.
(d12000 approx.

20. Option a

(a) Rs 18000(approx.)

 

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