Practice MCQ Questions and Answer on Interest

21.

If a sum of money double itself in 8 years, then the interest rate in percentage is ?

(A) $8 \frac{1}{2}$ %
(B) 10%
(C) $10 \frac{1}{2}$ %
(D) $12 \frac{1}{2}$ %

Solution: Money is double itself means interest is equal to money. $\begin{aligned} P = \frac{P \times 8 \times r}{100} \\ \Rightarrow r = \frac{100}{8} \\ \Rightarrow r = 12 \frac{1}{2} % \end{aligned}$

22.

Kruti took a loan at simple interest rate of 6 p.c.p.a. in the first year and it increased by 1.5 p.c.p.a. every year. If she pays Rs. 8190 as interest at the end of 3 years, what was her loan amount ?

(A) Rs. 35400
(B) Rs. 36000
(C) Rs. 36800
(D) Cannot be determined

Solution: Answer & Solution Answer: Option E Solution: Let the loan amount be Rs. x $\begin{aligned} Then, \\ \Rightarrow \frac{6 x}{100} + \frac{7.5 x}{100} + \frac{9 x}{100} = 8190 \\ \Rightarrow 22.5 x = 819000 \\ \Rightarrow x = 36400 \end{aligned}$

23.

If a certain sum of money becomes doubles at simple interest in 12 years, what would be the rate of interest per annum?

(A) $8 \frac{1}{3}$
(B) 10
(C) 12
(D) 14

Solution: Let, Principal, P = Rs. 100; Amount, A = Rs. 200; Time = 12 years; Interest = Rs. 100; Rate of interest $\begin{aligned} = \frac{Total Interest}{Given Time} \\ = \frac{100}{12} \\ = 8 \frac{1}{3} % \end{aligned}$

24.

A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?

(A) Rs. 400
(B) Rs. 500
(C) Rs. 700
(D) Rs. 800

Solution: Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y $\begin{aligned} Then, \\ \to 12 % of x + 10 % of y = 130 \\ \Rightarrow 12 x + 10 y = 13000 \\ \Rightarrow 6 x + 5 y = 6500. . . . . . (i) \\ And, \\ \to 10 % of x + 12 % of y = 134 \\ \Rightarrow 10 x + 12 y = 13400 \\ \Rightarrow 5 x + 6 y = 6700. . . . . . (ii) \\ Adding (i) and (ii), we get: \\ 11 (x + y) = 13200 \\ \Rightarrow x + y = 1200. . . . . . . (iii) \\ Subtracting (i) from (ii), \\ we get: - x + y = 200. . . . . . . (iv) \\ Adding (iii) and (iv), \\ we get : 2 y = 1400 o r y = 700 \\ Hence, \\ Amount invested at 12% \\ = (1200 - 700) \\ = Rs . 500 \end{aligned}$

25.

At which rate of simple interest does an amount become double in 12 years?

(A) $7 \frac{4}{5} %$
(B) $8 %$
(C) $8 \frac{1}{3} %$
(D) $7 \frac{1}{2} %$

Solution: $\begin{aligned} 1 = \frac{1 \times 12 \times r}{100} \\ r = 8 \frac{1}{3} % \end{aligned}$

26.

A person borrows some money for 5 years and ratio of loan amount : total interest amount is 5 : 2. Then find the ratio of loan amount : interest rate is equal to = ?

(A) 2 : 25
(B) 2 : 1
(C) 5 : 2
(D) 25 : 2

Solution: $\begin{aligned} Loan Amount : Total Interest \\ 5 : 2 \\ Principal \to 5 \\ Interest for 1 year \Rightarrow 2 \\ Interest for 5 year \Rightarrow 10 \\ 10 = \frac{5 \times R \times 5}{100} \\ R % = 40 % \\ = \frac{40}{100} = \frac{2}{5} \\ P : R = 5 : \frac{2}{5} \\ = 25 : 2 \end{aligned}$

27.

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she 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) Cannot be determined

Solution: $\begin{aligned} Let rate = R % and \\ Time = R years \\ Then, \frac{1200 \times R \times R}{100} = 432 \\ \Rightarrow 12 R^{2} = 432 \\ \Rightarrow R^{2} = 36 \\ \Rightarrow R = 6 \end{aligned}$

28.

What will be the simple interest on Rs. 700 at 9% per annum for the period from February 5, 1994 to April 18, 1994?

(A) Rs. 12.60
(B) Rs. 11.30
(C) Rs. 15
(D) Rs. 13

Solution: $\begin{aligned} Here, time interval is given as \\ February 5, 1994 to April 18, 1994 \\ = 73 days = \frac{73}{365} = 0.2 years . \\ Now interest = \frac{P T R}{100} \\ = \frac{700 \times 9 \times 0.2}{100} \\ = R s . 12.60 \end{aligned}$

29.

If the simple interest on a sum of money for 15 months at $7 \frac{1}{2}$ % per annum exceeds the simple interest on the same sum for 8 months at $12 \frac{1}{2}$ % per annum by Rs. 32.50, then the sum of money ( In Rs.) is ?

(A) Rs. 312
(B) Rs. 312.50
(C) Rs. 3120
(D) Rs. 3120.50

Solution: $\begin{aligned} T_{1} = 15 months \\ = \frac{15}{12} y e a r s \\ R_{1} = 7 \frac{1}{2} % = \frac{15}{2} % \\ T_{2} = 8 months \\ = \frac{8}{12} y e a r s \\ R_{2} = 12 \frac{1}{2} % = \frac{25}{2} % \\ Let the principal = P \\ According to the question, \\ \Leftrightarrow \frac{P \times 15 \times 15}{12 \times 2 \times 100} - \frac{P \times 25 \times 8}{12 \times 2 \times 100} = 32.50 \\ \Rightarrow \frac{225 P}{2400} - \frac{200 P}{2400} = 32.50 \\ \Rightarrow \frac{25 P}{2400} = 32.50 \\ \Rightarrow P = Rs 3120 \\ Hence required principal \\ = Rs . 3120 \end{aligned}$

30.

Rs. 6000 becomes Rs. 7200 in 4 years. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be = ?

(A) Rs. 8000
(B) Rs. 8250
(C) Rs. 9250
(D) Rs. 9000

Solution: $\begin{aligned} Principal Amount \\ \underset{+ 1200}{\underset{⏟}{6000 7200}} \\ By using formula, \\ Rate % \\ = \frac{1200}{6000} \times \frac{100}{4} \\ = 5 % \\ New rate % \\ = 5 \times \frac{3}{2} = 7 .5 % \\ Interest after 5 years \\ = \frac{6000 \times 7.5 \times 5}{100} \\ = Rs . 2250 \\ Hence, \\ amount \\ = Rs . (6000 + 2250) \\ = Rs 8250 \end{aligned}$

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Practice MCQ Questions and Answer on Interest

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