Simple and compound interest Questions and answers

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Aptitude

21). 2/3 part of my sum is lent out at 3%, 1/6 part is lent out at 6% and remaining part is lent out at 12%. All the three parts are lent out at simple interest. If the annual income is RS. 25, what is the sum?

A). RS.500

B). RS.650

C). RS.600

D). RS.450

View Answer

Correct Answer: RS.500

Let entire sum = P

According to the question

\( \Large \frac{2}{3}P\times 3\% +\frac{1}{6}P\times 6\% + [1- \left(\frac{2}{3}+\frac{1}{6}\right) ] P\times 12\% \)

=> \( \Large \frac{2P}{3}\times \frac{3}{100}+\frac{P}{6}\times \frac{6}{100}+[1-\frac{4+1}{6}]\frac{12P}{100} \)=25

=> \( \Large \frac{2P}{100}+\frac{P}{100}+\frac{2P}{100} \)=25

=> 5P=2500, P=500

22). A sum of RS. 1521 is lent out in two parts in such a way that the interest on one part at 10% for 5 yr is equal to that of another part at 8% for 10 yr. What will be the two parts of sum?

A). RS.926 and RS.595

B). RS.906 and RS.615

C). RS.916 and RS.605

D). RS.936 and RS.585

View Answer

Correct Answer: RS.936 and RS.585

Given, \( \Large T_{1} \) = 5 yr, \( \Large R_{1} \) =10% and \( \Large T_{2} \)=10yr and \( \Large R_{2} \)=8%

Let the first part = x

Then, second part = (1521 - x)

Now, according to the question,

\( \Large \frac{x\times 5\times 10}{100} \)=\( \Large \frac{(1521-x)\times 10\times 8}{100} \)

=> 5x=12168-8x

=> 13x=12168 => x=RS.936

and second parts = 1521 - 936 = RS.585

23). Harsha makes a fixed deposit of RS. 20000 in Bank of India for a period of 3 yr. If the rate of interest be 13% SI per annum charged half-yearly, what amount will he get after 42 months?

A). RS.27800

B). RS.28100

C). RS.29100

D). RS.30000

View Answer

Correct Answer: RS.29100

Given, time = 42 months

=> \( \Large \frac{42}{12}yr \)=\( \Large 3\frac{1}{2}yr \)

=> \( \Large \frac{7}{2}\times2 \)=7 half-yr,rate= \( \Large \frac{13}{2}\% \) half-yearly

SI=\( \Large \frac{20000\times 13\times 7}{100\times 2} \)=RS.9100

Amount(A)=20000+9100=RS.29100

24). The simple interest on RS. 4000 in 3 yr at the rate of x% per annum equals to the simple interest on RS. 5000 at the rate .of 12% per annum in 2 yr. The value of x is

A). 6%

B). 8%

C). 9%

D). 10%

View Answer

25). Suresh borrowed RS. 800 at 6% and Naresh borrowed RS. 600 at 10%. After how much time, will they both have equal debts?

A). \( \Large 15\frac{1}{3}yr \)

B). \( \Large 14\frac{1}{2}yr \)

C). \( \Large 18\frac{1}{3}yr \)

D). \( \Large 16\frac{2}{3}yr \)

View Answer

Correct Answer: \( \Large 16\frac{2}{3}yr \)

Given, \( \Large R_{1} \) = 6%, \( \Large R_{2} \) = 10%

According to the question,

\( \Large 800+\frac{800\times 6\times T}{100}=600+\frac{600\times 10\times T}{100} \)

800 + 48T = 600 + 60T

=> 12T = 200

=> 3T = 50

T = \( \Large \frac{50}{3}=16\frac{2}{3}yr \)

26). A sum of money amounts to RS. 2240 at 4% per annum simple interest in 3 yr. The interest on the same sum for 6 months at 3.5% per annum is

A). RS.30

B). RS.50

C). RS.35

D). RS.150

View Answer

Correct Answer: RS.35

If the sum be RS. P, then,

2240-P=\( \Large \frac{P\times 4\times 3}{100} \)

=> 2240=\( \Large \frac{12P}{100}+P \)

=> 2240=\( \Large \frac{112}{100}P \)

P=\( \Large \frac{2240\times 100}{112} \)=RS.2000

Now, required interest,

SI=\( \Large \frac{PRT}{100} \)=\( \Large 2000 \times \frac{7}{2}\times\frac{1}{2}\times\frac{1}{100} \)=Rs.35

27). A certain sum at simple interest amounts to RS. 1350 in 5 yr and to RS. 1620 in 8 yr. What is the sum?

A). RS.700

B). RS.800

C). RS.900

D). RS.1000

View Answer

Correct Answer: RS.900

Given, \( \Large A_{1} \) = RS.1350, \( \Large A_{2} \) = RS. 1620

\( \Large T_{1} \) =5yr and \( \Large T_{2} \) = 8yr

Let principal amount be RS. P.

In time = 8-5=3yr

Simple interest will be

1620 - 1350 = RS.270

R= \( \Large \frac{(A_{1}-A_{2})\times 100}{A_{1}T_{2}-A_{2}T_{1}} \)

= \( \Large \frac{(1620-1350)\times 100}{(1350\times 8-1620\times 5)} \)

= \( \Large \frac{270\times 100}{10800-8100}=\frac{27000}{2700} \)

=> R=10%

P=\( \Large \frac{SI\times 100}{R\times T}=\frac{270\times 100}{10\times 3} \)=RS.900

28). The principal on which a simple interest of RS. 55 will be obtained after 9 months at the rate of 3 2/3% per annum is

A). 1000

B). 1500

C). 2000

D). 2500

View Answer

Correct Answer: 2000

Let, principal = P

Given, SI = 55, Time t = 9 months =\( \Large \frac{9}{12}yr \)

Rate r = \( \Large 3\frac{2}{3}\% \)= \( \Large \frac{11}{3}\% \)

SI = \( \Large \frac{P\times r\times t}{100} \)

=> P = \( \Large \frac{100\times SI}{R\times T} \)

=> \( \Large \frac{55\times 100}{11\times 9}\times 3\times 12 \)=2000

Principal (P) = RS. 2000

29). The simple interest on a sum of money at 8% per annum for 6 yr is half the sum.What is the sum?

A). RS.4800

B). RS.6000

C). RS.8000

D). Data is inadequate

View Answer

30). In 4 yr, RS. 6000 amounts to RS. 8000. In what time at the same rate, will RS. 525 amount to RS. 700?

A). 2 yr

B). 3 yr

C). 4 yr

D). 5 yr

View Answer

Correct Answer: 4 yr

Amount = RS. 8000

Time (T) = 4 yr; Principal (P) = RS. 6000

Simple interest (SI) = (A-P)

= Amount - Principal

= 8000 - 6000 = RS. 2000

Rate (R) = ?

According to the formula,

SI = \( \Large \frac{P\times R\times T}{100} \)

=> 2000=\( \Large \frac{6000\times R\times 4}{100} \)

=> R=\( \Large \frac{2000\times 100}{6000\times 4} \)=\( \Large \frac{25}{3}\% \)

Now, again

Amount (A) = RS. 700

Principle (P) = RS. 525, Time (T) = ?

Rate (R) = \( \Large \frac{25}{3} \%\)

Simple interest = A - P

=> 700-525 = RS.175

Using formula, SI = \( \Large \frac{P\times R\times T}{100} \)

=> 175 = \( \Large \frac{525\times 25/3\times T}{100} \)

=> T = \( \Large \frac{175\times 100\times 3}{525\times 25} \) = 4yr

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