Practice MCQ Questions and Answer on Interest

21.

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 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

Solution: $\begin{aligned} Principal = R s . (\frac{100 \times 5400}{12 \times 3}) \\ = R s . 15000 \end{aligned}$

22.

The simple interest on a certain sum is one-eighth of the sum when the number of years is equal to half of the rate percentage per annum. Find the simple interest (in Rs.) on Rs. 15,000 at the same rate of simple interest for 8 years.

(A) 5,800
(B) 5,000
(C) 6,000
(D) 5,250

Solution: $\begin{aligned} Let sum = P \\ \frac{P \times r \times t}{100} = \frac{1}{8} P \\ r t = \frac{100}{8} = \frac{25}{2} . . . . . (i) \\ Since t = \frac{r}{2} \\ From equation (i) \\ r \times \frac{r}{2} = \frac{25}{2} \\ r = 5 % \\ If P = 1500 \\ t = 8 years \\ S .I . = \frac{P \times r \times t}{100} \\ = \frac{15000 \times 8 \times 5}{100} \\ = Rs . 6, 000 \end{aligned}$

23.

A Sum of Rs. 10,500 amounts to Rs. 13,825 in $3 \frac{4}{5}$ ÃÂÃÂ years at a certain rate percent per annum simple interest. What will be the simple interest on the same sum for 5 years at double the earlier rate?

(A) Rs. 8,670
(B) Rs. 8,750
(C) Rs. 8,470
(D) Rs. 8,560

24.

A man invested Rs. 5000 at some rate of simple interest and Rs. 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is

(A) 4% p.a.
(B) 5% p.a.
(C) $6 \frac{1}{4}$ % p.a.
(D) $8 \frac{1}{3}$ % p.a.

Solution: Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a. Then, $\begin{aligned} 5000 \times R \times 4 = 4000 \times (R + 1) \times 4 \\ \Rightarrow \frac{R + 1}{R} = \frac{5000 \times 4}{4000 \times 4} \\ \Rightarrow 1 + \frac{1}{R} = 1 + \frac{1}{4} \\ \Rightarrow R = 4 \\ Hence, \\ Required rate = 4 % p .a . \end{aligned}$

25.

Deepak invested an amount of Rs. 21250 for 6 years. At what rate of simple interest will be obtain the total amount of Rs. 26350 at the end of 6 years?

(A) 5 p.c.p.a
(B) 6 p.c.p.a
(C) 8 p.c.p.a
(D) 12 p.c.p.a

Solution: Answer & Solution Answer: Option E Solution: $\begin{aligned} P = Rs . 21250 \\ S .I . = Rs . (26350 - 21250) \\ = Rs . 5100 \\ T = 6 years \\ ∴ Rate = (\frac{100 \times 5100}{21250 \times 6}) % \\ = 4 % \end{aligned}$

26.

A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs. 5100 more. The sum is

(A) Rs. 1, 20, 000
(B) Rs. 1, 25, 000
(C) Rs. 1, 50, 000
(D) Rs. 1, 70, 000

Solution: $\begin{aligned} Let the sum be Rs . x and \\ original rate be R % \\ Then, \\ \Rightarrow \frac{x \times (R + 1) \times 3}{100} - \frac{x \times R \times 3}{100} = 5100 \\ \Rightarrow 3 R x + 3 x - 3 R x = 510000 \\ \Rightarrow 3 x = 510000 \\ \Rightarrow x = 170000. \\ Hence, \\ Sum = Rs .170000 \end{aligned}$

27.

On simple interest, a certain sum becomes Rs. 59,200 in 6 years and Rs. 72,000 in 10 years. If the rate of interest had been 2% more, then in how many years would the sum have become Rs. 76,000?

(A) 10
(B) 9
(C) 8
(D) 7

Solution: $\begin{matrix} P \overset{6 years}{\to} 59, 200 \\ P \overset{10 years}{\to} 72, 000 \end{matrix}$ $\begin{aligned} Difference 4 years \\ = (72, 000 - 59, 200) \\ = 12, 800 \\ 1 year = \frac{12, 800}{4} = 3, 200 \\ ∴ 6 years S .I . \\ = 3, 200 \times 6 = 19, 200 \\ P = 59, 200 - 19, 200 = 40, 000 \\ S .I . = \frac{P \times r \times t}{100} \\ 19, 200 = \frac{40, 000 \times r \times 6}{100} \\ r = 8 % \\ If r = 8 % + 2 % = 10 % \\ P = 40, 000 \\ t = ? \\ A = 76, 000 \\ ∴ S .I . = 36, 000 \\ 36, 000 = \frac{40, 000 \times 10 \times t}{100} \\ t = 9 years \end{aligned}$

28.

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

(A) 3.6%
(B) 4.5%
(C) 5%
(D) 6%

Solution: Answer & Solution Answer: Option E Solution: Let the original rate be R%. Then, new rate = (2R)%. Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. $\frac{1}{3}$ year(s). $\begin{aligned} ∴ \frac{725 \times R \times 1}{100} + \frac{362.50 \times 2 R \times 1}{100 \times 3} \\ = 33.50 \\ \Rightarrow (2175 + 725) R = 33.50 \times 100 \times 3 \\ \Rightarrow (2175 + 725) R = 10050 \\ \Rightarrow (2900) R = 10050 \\ \Rightarrow R = \frac{10050}{2900} = 3.46 \\ ∴ Original rate = 3.46 % \end{aligned}$

29.

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%

Solution: $\begin{aligned} S .I . = R s . (15500 - 12500) \\ = R s . 3000 \\ Rate = (\frac{100 \times 3000}{12500 \times 4}) % \\ = 6 % \end{aligned}$

30.

A man invested $\frac{1}{3}$ of his capital at 7%; $\frac{1}{4}$ at 8% and the remainder at 10%. If his annual income is Rs. 561, the capital is -

(A) Rs. 5400
(B) Rs. 6000
(C) Rs. 6600
(D) Rs. 7200

Solution: Let total capital be Rs. x Then, $\Rightarrow (\frac{x}{3} \times \frac{7}{100} \times 1) + (\frac{x}{4} \times \frac{8}{100} \times 1) +$ $(\frac{5 x}{12} \times \frac{10}{100} \times 1)$ $= 561$ $\begin{aligned} \Rightarrow \frac{7 x}{300} + \frac{x}{50} + \frac{x}{24} = 561 \\ \Rightarrow 51 x = (561 \times 600) \\ \Rightarrow x = (\frac{561 \times 600}{51}) \\ = 6600 \end{aligned}$

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Practice MCQ Questions and Answer on Interest

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