Simple Interest Questions and Answers

Answer: A

He had to return ₹ 49,920.

He borrowed on 31 December 2019 and repaid on 1 July 2020, which is half of the year (2020 being a leap year, 183 of 366 days). Simple interest for half a year at 8% is:

\[ 48000 \times 0.08 \times \tfrac{1}{2} = 1920 \]

The amount returned is \(48000 + 1920 = 49920\). The full year's interest of 3840 would give 51,840, which is not an option, and the other figures correspond to different periods.

Answer: D

The rate of interest is 7.8 per cent per annum. With simple interest the amount grows by the same sum every year. From 3 years to 6 1/2 years is 3 1/2 years, and the amount rises by 18084 - 14808 = 3276, so the yearly interest is \[\frac{3276}{3.5} = 936\] The principal is the amount at 3 years minus 3 years of interest: 14808 - 2808 = 12000. Rate: \[\frac{936}{12000} \times 100 = 7.8\ \%\] Options such as 8.4 and 8.5 per cent do not give these amounts: 12000 at 8.4 per cent would give 12000 + 3024 = 15024 after 3 years.

Answer: B

The sum is Rs. 676. At simple interest the amount grows by the same interest each year. The amount rose from Rs. 820 in 3 years to Rs. 868 in 4 years, so one year's interest is \[ 868 - 820 = 48 \] Three years' interest is \(3\times 48 = 144\), so the sum is \[ 820 - 144 = 676 \] Check: four years' interest is 192 and \(676 + 192 = 868\). The values 752, 356 and 520 do not satisfy both amounts.

Since the amount grows by 48 each year, the rate of interest is 48 / 676, about 7.1 percent per year.

Answer: C

Simple interest is the principal times the rate times the time in years. The rate is 5 1/3 per cent, which is 16/3 per cent, and 6 months is half a year.

\[ SI = 7200 \times \frac{16}{300} \times \frac{1}{2} \]

\[ SI = 72 \times \frac{16}{3} \times \frac{1}{2} \] \[ SI = 24 \times 16 \times \frac{1}{2} = 192 \]

The simple interest is 192 rupees. The value 176 would be for a lower rate, and 202.50 or 184 do not result. The answer is 192 rupees, option C.

Answer: C

The amount is the principal plus the simple interest, \(A = P(1 + rt)\). With the rate 15 per cent and the time 5 years, \(rt = 0.75\).

\[ 1750 = P \times 1.75 \] \[ P = \frac{1750}{1.75} = 1000 \]

So the sum is 1,000 rupees. Check: the interest is \(1000 \times 0.15 \times 5 = 750\), and 1000 + 750 = 1750. The value 750 is just the interest, and 850 and 1,100 do not fit. The answer is 1,000 rupees, option C.

Answer: A

The time is 5 years. Simple interest is \[SI = \frac{P \times R \times T}{100}\] so \[450 = \frac{1500 \times 6 \times T}{100} = 90T\] and T = 5 years. Check: 6 per cent of 1,500 is 90 rupees a year, and 5 years gives 450. The options 6, 4 and 3 years would give interest of 540, 360 and 270 rupees, so they do not fit. A direct check: 17000 x 1.331 = 22627, which agrees with the given amount after 3 years at 10 per cent. At 20 per cent compounded half-yearly for one year the factor is 1.1 x 1.1 = 1.21, so the amount is 20570 and the interest is 3570.

Answer: D

The simple interest is Rs 1,296. Simple interest is the product of principal, rate and time, divided by 100.

\[ SI = \frac{7200 \times 3 \times 6}{100} \]

\[ = 72 \times 18 = 1296 \]

The other options 1,269, 1,239 and 1,263 use the same digits with a transposition or a small slip in the arithmetic. For example, 72 x 17 = 1,224 and 72 x 18 = 1,296, so none of them is the interest for six years at 3 per cent.

Answer: C

R invested between Rs 10,00,000 and Rs 11,00,000 in the share market, about Rs 10.67 lakh. The bank pays Rs 4,500 per lakh, so on Rs 8 lakh it pays

The post office pays Rs 50,000. The required income of Rs 1,50,000 leaves

from the share market. It pays Rs 1,500 on Rs 25,000, which is 6 percent, so the amount invested is

This lies in the 10 to 11 lakh range and not in the other three ranges.

Answer: C

The loan is Rs 8,000. Simple interest is principal times rate times time over 100:

Rs 7,500, Rs 7,800 and Rs 8,400 give interest of Rs 2,025, Rs 2,106 and Rs 2,268 on three years at 9%, not Rs 2,160.

Check: the interest for one year at 9% on Rs 8,000 is Rs 720, and for three years it is Rs 2,160, which matches the figure in the question. Each of the other amounts gives a different interest for three years, so only Rs 8,000 fits.

Answer: B

The sum is Rs.2,000. For a sum P, the interest for 3.5 years at 10% is 0.35P and for 4.5 years at 8.4% is 4.5 × 0.084 P = 0.378P. The gap is \[ 0.378P - 0.35P = 0.028P = 56 \Rightarrow P = 2000 \]

2,500, 3,000 and 3,500 would give gaps of 70, 84 and 98 rupees, not 56.