Aptitude Simple And Compound Interest Problems With Solutions

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Aptitude Simple And Compound Interest Problems With Solutions

Simple And Compound Interest Problems With Solutions

Aptitude Simple And Compound Interest Problems With Solutions

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

 

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

 

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

Option B

Time = [100 × 81 / 450 × 4.5  ] years = 4 years

 

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

Option D

 

S.I. = Rs. (15500 ⎯ 12500) = Rs.3000

 

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

 

 

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

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%

 

 

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

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%

 

 

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

Option C

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

 

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

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

 

 

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

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

 

 

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

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

 

 

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

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

 

 

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

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

 

 

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

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

 

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

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

 

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

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

 

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

Option B

Let rate = R% and time = R years

Then, [1200 × R  × R / 100] = 432

12 r2 = 432

R2 = 36

R = 6

 

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

Ans.

(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

 

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

Ans.

 (b) 20years

 

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%

Ans.

 (d) 12 %

Hint: 

 

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%

Ans.

 (b) 10%

Hint:

 

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.

Ans.

(a) Rs 18000(approx.)

 

In one year, the population of a village increased by 10% and in the next year, it decreased by 10%. If the end of the 2nd year, the population was 7920, what was it in the beginning?

(a) 8500

(b) 8000

(c) 8100

(d) 8400

Ans

(b) 8000

Hint:

 

 

If the amount is 2¼ times the sum after 2 years at compound interest, the rate of interest per annum is

(a) 25%

(b) 45%

(c) 40%

(d) 50%

Ans

 (d) 50%

 

A sum of money grows to Rs 200 after 1st year and to Rs 220 after 2nd year, at compound interest. The rate % is

(a) 15

(b) 10

(c) 25

(d) 12

Ans

(b) 10

Hint:

 

 

How much more would Rs 20,000 fetch, after two years, if it is put at 20% p.a. compound interest Payable half yearly than if it is put at 20% p.a. compound interest payable yearly?

(a) 482

(b) 424

(c) 842

(d) 512

Ans

(a) Rs 482 

Hint: Required amount 

 

Find the principal of the interest compounded at the rate of 10% per annum for the two years is Rs. 420.

  1. Rs. 2000
  2. Rs. 2200
  3. Rs. 1000
  4. Rs. 1100
  5. None of These

Ans

 

 

At what percentage per annum, will Rs 10,000 amount to 17, 280 in three years?(Compound interest being reckoned)

  1. 20%
  2. 14%
  3. 24%
  4. 11%
  5. None of These

Ans

 

What is the rate of simple interest for the first 4 years if the sum of Rs. 360 become Rs. 540 in 9 years and the rate of interest for the last 5 years in 6%?

  1. 4%
  2. 5%
  3. 3%
  4. 6%
  5. None of These

Ans

 

A sum of money doubles itself in 5 years. In how many years will it become four fold (if interest is compounded)

  1. 15
  2. 10
  3. 20
  4. 12
  5. None of These

Ans

 

Rakesh took a loan for 6 years at the rate of 5% p.a. S.I. if the total interest paid was Rs. 1230. the principal was:

  1. Rs 4100
  2. Rs 4920
  3. Rs 5000
  4. Rs 5300
  5. None of Thse

Ans

 

A sum of money was lent at simple interest at 11% p.a. for 3½ years and 4½ years respectively. If the difference in interest for two periods was Rs. 41250, the sum is.

  1. Rs. 3250
  2. Rs. 3500
  3. Rs. 3750
  4. Rs. 4250
  5. None of These

Ans