Practice MCQ Questions and Answer on Interest

61.

A sum of Rs. 7930 is divided into 3 parts and given at loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of = ?

(A) Rs. 2800
(B) Rs. 3050
(C) Rs. 2750
(D) Rs. 2760

Solution: According to the question, $A + (\frac{A \times 5 \times 2}{100}) =$ $B + (\frac{B \times 5 \times 3}{100}) =$ $C + (\frac{C \times 5 \times 4}{100})$ 110A = 115B = 120C 22A = 23B = 24X Ratio of amount ( by using L.C.M. of 22, 23 and 24) $\begin{aligned} 276 : 264 : 253 \\ A's loan = \frac{276}{793} \times 7930 \\ = Rs . 2760 \end{aligned}$

62.

A sum of Rs. 1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part ( in Rupees) is ?

(A) Rs. 60
(B) Rs. 65
(C) Rs. 70
(D) Rs. 40

Solution: $\begin{aligned} Principal = Rs . 1750 \\ Let the first part = x \\ Hence second part \\ = (1750 - x) \\ According to the question, \\ \Rightarrow x \times \frac{8}{100} \times 1 = (1750 - x) \times \frac{6}{100} \times 1 \\ \Rightarrow 4 x = 5250 - 3 x \\ \Rightarrow 7 x = 5250 \\ \Rightarrow x = 750 \\ First part = Rs . 750 \\ ∴ Second part \\ = Rs . (1750 - 750) \\ = Rs . 1000 \\ Required interest \\ = 750 \times \frac{8}{100} \\ = Rs . 60 \end{aligned}$ Alternate Note : In such type of questions to save your valuable time follow the given below method. Let, Principal = 100 units in both cases 1st part 2nd part Total Principal → 100×3 : 100×4 +→ 700 units Interest → 8×3 : 6×4 Note : Interest is same in both cases According to the question, $\begin{aligned} 700 units = Rs . 1750 \\ 1 unit = Rs . \frac{1750}{700} \\ 24 units = Rs . \frac{1750}{700} \times 24 \\ = Rs . 60 \\ Hence, required interest \\ = Rs . 60 \end{aligned}$

63.

A sum of Rs. 1440 is lent out in three parts in such away that the interests on first part at 2% for 3 years, second part at 3% for 4 years and third part at 4% for 5 years are equal. Then the difference between the largest and the smallest sum is -

(A) Rs. 200
(B) Rs. 400
(C) Rs. 460
(D) Rs. 560

Solution: Let the parts be Rs. x, Rs. y and Rs. [1440 - (x + y)]. Then, $\begin{aligned} = \frac{x \times 2 \times 3}{100} = \frac{y \times 3 \times 4}{100} \\ = \frac{[1440 - (x + y)] \times 4 \times 5}{100} \\ ∴ 6 x = 12 y o r x = 2 y . \\ S o, \frac{x \times 2 \times 3}{100} = \frac{[1440 - (x + y)] \times 4 \times 5}{100} \\ \Leftrightarrow 12 y = (1440 - 3 y) \times 20 \\ \Rightarrow 72 y = 28800 \\ \Rightarrow y = 400 \\ First part = x = 2 y = Rs . 800, \\ Second part = Rs . 400 \\ Third part \\ = Rs . [1440 - (800 + 400)] \\ = Rs . 240. \\ ∴ Required difference \\ = Rs . (800 - 240) \\ = Rs .560 \end{aligned}$

64.

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

65.

Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.

(A) 8%
(B) 9%
(C) 10%
(D) 11%

Solution: $\begin{aligned} Let rate is R % \\ We have, \\ I = \frac{P T R}{100} \\ Here, 1500 = \frac{5000 \times 3 \times R}{100} \\ Thus, R = 10 % \end{aligned}$

66.

The difference between simple and compound interest for the fourth year is Rs. 7280 at 20% p.a. What is the principal sum?

(A) 10000
(B) 50000
(C) 70000
(D) 40000

Solution: Difference between Compound interest and Simple interest for the fourth year is Rs. 7280 $\begin{aligned} P {(\frac{6}{5})}^{3} (\frac{1}{5}) - \frac{P}{5} = 7280 \\ \frac{P}{5} [{(\frac{6}{5})}^{3} - 1] = 7280 \\ \frac{P}{5} [\frac{216}{125} - 1] = 7280 \\ \frac{P}{5} \times \frac{91}{125} = 7280 \\ ∴ P = 50000 \end{aligned}$

67.

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

68.

In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly?

(A) 6 months
(B) 1 year
(C) $1 \frac{1}{2}$ years
(D) 3 months

Solution: $\begin{aligned} P = R s . 3300 \\ A = R s . 3399 \\ R = 6 % per annum \\ Let the time be n years . \\ Compound interest is taken half - yearly . \\ A = P \times {[1 + (\frac{R}{2} \times 100)]}^{2 n} \\ 3399 = 3300 {(1 + \frac{3}{100})}^{2 n} \\ {(1.03)}^{2 n} = \frac{3399}{3300} \\ {(1.03)}^{2 n} = {(1.03)}^{1} \\ T h u s, 2 n = 1 y e a r \\ n = \frac{1}{2} year = 6 months \end{aligned}$

69.

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

(A) 1 : 3
(B) 1 : 4
(C) 2 : 3
(D) Data inadequate

Solution: Let the principal be P and rate of interest be R%. Therefore Required ratio $\begin{aligned} = \frac{\frac{P \times R \times 6}{100}}{\frac{P \times R \times 9}{100}} \\ = \frac{6 P R}{6 P R} \\ = \frac{6}{9} \\ = 2 : 3 \end{aligned}$

70.

A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is

(A) Rs. 500
(B) Rs. 600
(C) Rs. 700
(D) Rs. 710

Solution: $\begin{aligned} S .I . for 5 years \\ = Rs . (1020 - 720) \\ = Rs . 300 \\ S .I . for 2 years \\ = Rs . (\frac{300}{5} \times 2) \\ = Rs . 120 \\ ∴ Principal \\ = Rs . (720 - 120) \\ = Rs . 600 \end{aligned}$

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Practice MCQ Questions and Answer on Interest

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