Interest - Aptitude MCQ Questions and Solutions with Explanations

1.

Find the simple interest on Rs. 2,700 for 8 months at 5 paisa per rupee per month?

(A) Rs. 950
(B) Rs. 720
(C) Rs. 540
(D) Rs. 1,080

Solution: $\begin{aligned} Rate = \frac{5 paisa}{1 rupee} = 5 % \\ Time = 8 months \\ S .I . = \frac{2700 \times 5 \times 8}{100} = 1080 \end{aligned}$

2.

The principal which gives Rs 1 interest per day at a rate of 5% simple interest per annum is = ?

(A) Rs. 5000
(B) Rs. 35500
(C) Rs. 7300
(D) Rs. 3650

Solution: $\begin{aligned} According to the question, \\ Interest = Rs . 1 per day \\ ∴ Interest in one year \\ = 1 \times 365 = Rs . 365 \\ ∴ S .I . = \frac{P \times T \times R}{100} \\ \Rightarrow 365 = \frac{P \times 5 \times 1}{100} \\ \Rightarrow P = \frac{365 \times 100}{5} \\ \Rightarrow P = Rs . 7300 \end{aligned}$

3.

What is the amount of equal installment, if a sum of Rs. 1428 due 2 years hence has to be completely repaid in 2 equal annual installments starting next year?.

(A) 700
(B) 800
(C) 650
(D) cannot be determined

Solution: As short - cut of installment for 2 installments is given by Installment = $\frac{P}{(\frac{100}{100} + R) + {(\frac{100}{100} + R)}^{2}}$ There is the need of rate (R) which is unavailable in the question. so, we cannot determine the answer

4.

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

5.

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

6.

A sum of money was invested at a certain rate of simple interest for 2 years. Had it been invested at 1% higher rate, it would have fetched Rs. 24 more interest. The sum of money is ?

(A) Rs. 1200
(B) Rs. 1050
(C) Rs. 1000
(D) Rs. 9600

Solution: More interest paid in 2 years $\begin{aligned} = 2 \times 1 = 2 % \\ According to the question, \\ 2 % of sum = Rs . 24 \\ 1 % of sum = Rs . \frac{24}{2} \\ Total sum \\ = Rs . \frac{24}{2} \times 100 \\ = Rs . 1200 \end{aligned}$

7.

A certain sum doubles in 7 years at simple interest. The same sum under the same interest rate will become 4 times in how many years = ?

(A) 14 years
(B) 28 years
(C) 21 years
(D) 10 years

Solution: $\begin{aligned} \frac{(n - 1)}{t_{1}} = \frac{(m - 1)}{t_{2}} \\ \frac{1}{7} = \frac{3}{t_{2}} \\ t_{2} = 21 years \end{aligned}$

8.

A digital note-pad is available for Rs. 25,000 cash or Rs. 2,500 down payment followed by 4 equal monthly instalments. If the rate of interest charged is 24% per annum simple interest, what is the monthly instalment (in ., rounded off to the nearest tens)?

(A) Rs. 5,800
(B) Rs. 5,790
(C) Rs. 5,890
(D) Rs. 5,900

Solution: $\begin{aligned} Cash amount = 25000 \\ Down payment = 2500 \\ Remaining amount = 22500 \\ Rate = 24 % p .a \\ 12 month \to 24 % \\ \to \frac{24}{12} \times 100 = \frac{1}{50} \\ 4 month \to 8 % \\ \Rightarrow Total amount = 22500 \times \frac{108}{100} \\ = 24300 \end{aligned}$ $\begin{matrix} 50 & - & 50 \\ 50 & - & 51 \\ 50 & - & 52 \\ 50 & - & \underset{______}{53} \\ 206 \end{matrix}$ $\begin{aligned} EMI = \frac{24300 \times 50}{206} \\ = 5898.05 \\ = 5900 \end{aligned}$

9.

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

10.

The amount Rs. 2100 become Rs. 2352 in 2 years at simple interest. If the interest rate is decreased by 1% , what is the new interest ?

(A) Rs. 210
(B) Rs. 220
(C) Rs. 242
(D) Rs. 252

Solution: $\begin{aligned} According to the question, \\ Principal = Rs . 2100 \\ Amount = Rs . 2352 \\ SI = A - P \\ = 2352 - 2100 \\ = Rs . 252 \\ Time = 2 years, \\ Let rate = R% \\ R = \frac{252}{2100} \times \frac{100}{2} = 6% \\ New rate of interest \\ = (6 - 1) \\ = 5% \\ New interest \\ = \frac{2100 \times 5 \times 2}{100} \\ = Rs . 210 \\ Hence required interest \\ = Rs . 210 \end{aligned}$

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