Practice MCQ Questions and Answer on Interest

111.

A person who pays income tax at the rate of 4 paise per rupee, find that fall of interest rate (income tax) from 4% to 3.75% diminishes his net yearly income by Rs. 48. What is his capital ?

(A) Rs. 24000
(B) Rs. 25000
(C) Rs. 20000
(D) Rs. 18000

Solution: Capital after paying income tax $\begin{aligned} \Rightarrow 4 % - 3 .75 % = 48 \\ \Rightarrow 0 .25 % = 48 \\ 100 % = \frac{48}{0.25} \times 100 \\ = 19200 \end{aligned}$ ⇒ Capital without paying income tax ⇒ 19200 = Capital × 96% Net capital = 20000

112.

A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is = ?

(A) $5 \frac{1}{2}$ %
(B) 8 %
(C) 7 %
(D) 6 %

Solution: $\begin{aligned} Time = 2 years 3 months \\ = 2 + \frac{3}{12} = \frac{9}{2} years \\ We know SI = \frac{P \times T \times R}{100} \\ P = Rs 1600, \\ T = \frac{9}{4} years, \\ SI = Rs 252 \\ Put values in the formula , \\ \Rightarrow 252 = \frac{1600 \times R \times 9}{100} \\ \Rightarrow 252 = 36 R \\ \Rightarrow R = \frac{252}{36} = 7 % \end{aligned}$

113.

A sum of money becomes Rs. 20925 in 2 years and Rs. 24412.50 in 5 years. Find the rate of interest and the sum of money.

(A) 6.25%, Rs. 18600
(B) 6.75%, Rs. 17775
(C) 7%, Rs. 18000
(D) 8%, Rs. 17560

Solution: $\begin{aligned} S .I . for 3 years \\ = Rs . (24412.50 - 20925) \\ = Rs . 3487.50 \\ S .I . for 2 years \\ = Rs . (\frac{3487.50}{3} \times 2) \\ = Rs . 2325 \\ ∴ Principal \\ = Rs . (20925 - 2325) \\ = Rs . 18600 \\ Hence, \\ rate = (\frac{100 - 2325}{18600 \times 2}) % \\ = 6.25 % \end{aligned}$

114.

A person invested a total of Rs. 57,500 at 4%, 5% and 8% per annum simple interest. At the end of the year, he received equal interest in all the three cases. The amount invested at 5% was:

(A) Rs. 20,000
(B) Rs. 20,750
(C) Rs. 25,000
(D) Rs. 37,500

Solution: $\begin{aligned} \frac{1}{4} : \frac{1}{5} : \frac{1}{8} \\ 10 : 8 : 5 \\ Amount invested at 5 % \\ = \frac{8}{23} \times 57, 500 \\ = 20, 000 \end{aligned}$

115.

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

(A) 5%
(B) 8%
(C) 12%
(D) 15%

Solution: $\begin{aligned} S .I . for 3 years \\ = Rs . (12005 - 9800) \\ = Rs . 2205 \\ S .I . for 5 years \\ = Rs . (\frac{2205}{3} \times 5) \\ = Rs . 3675 \\ ∴ Principal \\ = Rs . (9800 - 3675) \\ = Rs . 6125 \\ Hence, rate = (\frac{100 \times 3675}{6125 \times 5}) % \\ = 12 % \end{aligned}$

116.

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both as interest. The rate of interest per annum is = ?

(A) 7%
(B) 5%
(C) $7 \frac{1}{8}$ %
(D) 10%

Solution: $\begin{aligned} Let the rate % = R \\ According to the question, \\ \frac{5000 \times 2 \times R}{100} + \frac{3000 \times 4 \times R}{100} = 2200 \\ \Rightarrow 100 R + 120 R = 2200 \\ \Rightarrow 220 R = 2200 \\ \Rightarrow R = 10 % \\ Hence required rate % \\ = 10 % \end{aligned}$

117.

Rs. 6200 amounts to Rs. 9176 in 4 years at simple interest. If the interest rate is increased by 3% it would amount to how much?

(A) Rs. 8432
(B) Rs. 9820
(C) Rs. 9920
(D) Rs. 10920

Solution: $\begin{aligned} P = Rs . 6200 \\ S .I . \\ = Rs . (9176 - 6200) \\ = Rs . 2976 \\ T = 4 years \\ ∴ Rate \\ = (\frac{100 \times 2976}{6200 \times 4}) % \\ = 12 % \\ New rate \\ = (12 + 3) % \\ = 15 % \\ New S .I . \\ = Rs . (\frac{6200 \times 15 \times 4}{100}) \\ = Rs. 3720 \\ New amount \\ = Rs . (6200 + 3720) \\ = Rs . 9920 \end{aligned}$

118.

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

119.

Jhon invested a sum of money at an annual simple interest rate of 10%. At the end of four years the amount invested plus interest earned was Rs. 770. The amount invested was = ?

(A) Rs. 650
(B) Rs. 350
(C) Rs. 550
(D) Rs. 500

Solution: Let the amount invested = Rs. P According to the question, $\begin{aligned} P + \frac{P \times 10 \times 4}{100} = 770 \\ \Rightarrow P + \frac{4 P}{10} = 770 \\ \Rightarrow \frac{14 P}{10} = 770 \\ \Rightarrow P = \frac{770 \times 10}{14} \\ \Rightarrow P = Rs 550 \end{aligned}$ Hence, required invested amount = Rs. 550 Alternate $\begin{aligned} 10 % = \frac{1 \to Interest}{10 \to Principal} \\ Interest in 4 years \\ = 1 \times 4 \\ = 4 \\ Amount = \\ = (Interest + Principal) \\ = 4 + 10 \\ = 14 \\ According to the question, \\ 14 units = 770 \\ 1 unit = \frac{770}{14} \\ 10 units = \frac{770}{14} \times 10 \\ = Rs . 550 \\ The amount invested \\ = Rs . 550 \end{aligned}$

120.

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

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Practice MCQ Questions and Answer on Interest

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