Practice MCQ Questions and Answer on Interest

21.

The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is:

(A) Rs. 4800
(B) Rs. 6000
(C) Rs. 8000
(D) Date inadequate

Solution: $\begin{aligned} Let sum = x . \\ Then, \\ S .I . = \frac{x}{2} \\ ∴ \frac{x}{2} = \frac{x \times 8 \times 6}{100} \end{aligned}$ Clearly, data is inadequate.

22.

A sum amounts to Rs. 14,395.20 at 9.25% p.a. simple interest in 5.4 years. What will be the simple interest on the same sum at 8.6% p.a. in 4.5 years?

(A) Rs. 3,715.20
(B) Rs. 3,627
(C) Rs. 3,797.76
(D) Rs. 3,672

Solution: $\begin{aligned} \frac{P \times 5.4 \times 9.25}{100} = (14395.20 - P) \\ P = 9600 \\ \frac{9600 \times 8.6 \times 4.5}{100} = SI \\ SI = 3715.20 \end{aligned}$

23.

Tushar borrowed a sum of Rs. 12000 at 15% per annum from a money - lender on 13^th January, 1987 and return the amount on 8^th June, 1987 to clear his debt. Then the amount paid by Tushar to the money - lender to clear his debt was = ?

(A) Rs. 15000
(B) Rs. 11394
(C) Rs. 12720
(D) Rs. 13650

Solution: Time = 18 + 28 + 31 + 30 + 31 + 8 = 146 days $\begin{aligned} Simple Interest \\ = \frac{12000 \times 15 \times 146}{365 \times 100} \\ = Rs . 720 \\ ∴ Amount will be \\ = Rs . (12000 + 720) \\ = Rs . 12720 \end{aligned}$

24.

A sum of money becomes $\frac{7}{4}$ of itself in 6 years at a certain rate of simple interest. Find the rate of interest.

(A) 12%
(B) $12 \frac{1}{2}$ %
(C) 8%
(D) 14%

Solution: $\begin{aligned} Let sum i s Rs . 100, \\ Then it become \frac{7}{4} times \\ i . e . Rs . \frac{700}{4} in 6 years . \\ Interest = \frac{700}{4} - 100 = R s . \frac{300}{4} \\ Hence, \\ Rate = \frac{Total interest}{Given time} \\ = \frac{300}{4} \times 6 \\ = 12 \frac{1}{2} % \end{aligned}$

25.

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

26.

A person borrows Rs. 1,00,000 from a bank at 10% per annum simple interest and clears the debt in five years. If the instalment paid at the end of the first, second, third and fourth years to clear the debt are Rs. 10,000, Rs. 20,000, Rs. 30,000 and Rs. 40,000, respectively, what amount should be paid at the end of the fifth year to clear the debt?

(A) Rs. 38,250
(B) Rs. 39,490
(C) Rs. 40,450
(D) Rs. 36,450

Solution: $\begin{aligned} Interest at the end of 1^{st} year \\ = \frac{1, 00, 000 \times 10}{100} \\ = 10, 000 \\ Paid amount = 10, 000 \\ Rest amount \\ = 1, 10, 000 - 10, 000 \\ = 1, 00, 000 \\ Interest for 2^{nd} year = 10, 000 \\ Amount paid = 20, 000 \\ Remaining amount \\ = 1, 10, 000 - 20, 000 \\ = 90, 000 \\ Interest for 3^{rd} year = 9, 000 \\ Amount paid = 30, 000 \\ Remaining amount \\ = 99, 000 - 30, 000 \\ = 69, 000 \\ Interest for 4^{th} year = 6, 900 \\ Amount paid = 40, 000 \\ Remaining amount \\ = 75, 900 - 40, 000 \\ = 35, 900 \\ Interest for 5^{th} year \\ = \frac{35, 900 \times 10}{100} \\ = 3, 590 \\ Amount paid at the end of 5^{th} year \\ = 35, 900 + 3, 590 \\ = 39, 490 \end{aligned}$

27.

A person borrowed 1,200 at 8% per annual and Rs. 1,800 at 10% per annum, as simple interest for the same period. He had to pay Rs. 1380 in all as interest. Find the time? (in year)

(A) 4 years
(B) 5 years
(C) 6 years
(D) 10 years

Solution: $\begin{aligned} \frac{1200 \times t \times 8}{100} + \frac{1800 \times t \times 10}{100} = 1380 \\ 96 t + 180 t = 1380 \\ 276 t = 1380 \\ t = 5 \end{aligned}$

28.

A certain scheme of investment in simple interest declares that it triples the investment in 8 years. If you want to quadruple the money through that scheme for how many years you have to invest for = ?

(A) 11 years 6 months
(B) 10 years 8 months
(C) 10 years
(D) 12 years

Solution: $\begin{aligned} P + \frac{P \times r \times t}{100} = 3 P \\ \Rightarrow 1 + \frac{r t}{100} = 3 \\ \Rightarrow \frac{rt}{100} = 2 \\ \Rightarrow r = \frac{2 \times 100}{8} = 25 % \\ so, (1 + \frac{rt}{100}) = 4 \\ \Rightarrow \frac{rt}{100} = 3 \\ \Rightarrow t = \frac{3 \times 100}{25} \\ \Rightarrow t = 12 years \end{aligned}$

29.

Consider the following statements
If a sum of money is lent at simple interest, then the
I - money gets doubled in 5 years if the rate of interest is $16 \frac{2}{3}$ %
II - money gets doubled in 5 years if the rate of interest is 20%.
III - money becomes four times in 10 years if it gets doubled in 5 years.

(A) I and III are correct
(B) II alone is correct
(C) III alone is correct
(D) II and III are correct

Solution: $\begin{aligned} Let sum be x . \\ Then, \\ S .I . = x \\ I - Time \\ = \frac{100 \times x}{x \times \frac{50}{3}} \\ = 6 years(false) \\ II - Time \\ = \frac{100 \times x}{x \times 20} \\ = 5 years(True) \\ III - Suppose sum = x . \\ Then, S .I . = x \\ Time = 5 years . \\ Rate = (\frac{100 \times x}{x \times 5}) % \\ = 20 % . \\ Now, sum = x, S .I . = 3 x and Rate = 20 % \\ ∴ Time = (\frac{100 \times 3 x}{x \times 20}) years \\ = 15 years (false) \\ So, B alone is correct . \end{aligned}$

30.

A person borrows Rs. 5000 for 2 year at 4% p.a. simple interest. He immediately lends it to another person at $6 \frac{1}{4}$ % p.a. for 2 years. Find his gain in the transaction per year.

(A) Rs. 112.50
(B) Rs. 125
(C) Rs. 150
(D) Rs. 167.50

Solution: $\begin{aligned} Gain in 2 years \\ = (5000 \times \frac{25}{4} \times \frac{2}{100}) - (\frac{5000 \times 4 \times 2}{100}) \\ = Rs . (625 - 400) \\ = Rs . 225 \\ ∴ Gain 1 year = Rs . (\frac{225}{2}) \\ = Rs . 112.50 \end{aligned}$

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Practice MCQ Questions and Answer on Interest

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