Simple Interest Questions and Answers

Answer: A

The time is 10 years. For the sum to become 1.5 times itself the interest must be half the sum, 4,800 rupees on Rs 9,600. Simple interest = 9600 x 5 x t / 100 = 480t, so 480t = 4800 and t = 10 years. 8, 11 and 12 years give interest of 3,840, 5,280 and 5,760 rupees. Here the interest needed is 50 per cent of the principal, and at 5 per cent a year each year earns 5 per cent of the principal, so the time is 50 divided by 5 = 10 years, whatever the principal is.

Answer: C

The amount is 6,655. At simple interest of 7.4 % for 5 years, the amount is the principal times 1 + 0.37 = 1.37.

\[ P = \frac{7535}{1.37} = 5500 \]

For one year at 20 % compounded half-yearly, the rate is 10 % for each of two half-years.

\[ A = 5500 \times (1.1)^2 = 5500 \times 1.21 = 6655 \]

The options 6,413, 6,534 and 7,920 do not equal 5500 times 1.21, so the third option is the answer. As a check, the interest in 5 years is 37 % of 5500, which is 2035, and 5500 + 2035 = 7535, the amount given in the question.

Answer: B

It will take 4 months.

Simple interest is P × R × T / 100. With P = 3500, R = 6 and an interest of 70, the time is

\[ T=\frac{70\times100}{3500\times6}=\frac{1}{3}\text{ year} \]

\[ \frac{1}{3}\text{ year}=4\text{ months} \]

2 months would earn 35, 8 months 140 and 6 months 105 as interest.

Per year the interest on 3500 at 6% is 210. A year therefore earns 210, a month earns 17.5 and 70 needs 4 months. The option '6 month' would earn 105 and 8 months would earn 140.

Answer: C

The sum is ₹ 9,600. Let the sum be \(P\). Simple interest for 10 years at 9.5% is \(0.95P\). The amount for \(3\frac{1}{2}\) years at 7% simple interest is \[ P\left(1 + \frac{7\times 3.5}{100}\right) = 1.245P \] The interest is less than that amount by 2,832: \[ 1.245P - 0.95P = 0.295P = 2832 \] \[ P = \frac{2832}{0.295} = 9600 \] Check: 0.95 × 9600 = 9120 and 1.245 × 9600 = 11952, which differ by 2832. The other sums do not give that difference.

Answer: A

The simple interest is 2176.

Simple interest = P × R × T / 100.

\[ \frac{6800\times8\times4}{100}=2176 \]

2167, 2076 and 2716 are different arrangements of the digits and do not equal the product.

The yearly interest is 8% of 6,800 = 544, and for 4 years it is 4 × 544 = 2,176. The principal is not added, since simple interest is only the interest. The amount would be 8,976.

Answer: B

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The two investments share the rate and the four years, so the Rs. 130 gap comes entirely from the Rs. 250 difference in principal.

\[ \frac{(2250 - 2000) \times R \times 4}{100} = 130 \]

\[ \frac{250 \times 4R}{100} = 10R = 130 \quad\Longrightarrow\quad R = 13\% \]

Working out each interest separately gives the same answer but needs two calculations instead of one.

Answer: D

Let \( p \) be the part at 5%; the rest, \( 2500 - p \), earns 6%.

\[ 0.05p + 0.06(2500 - p) = 140 \]

\[ 0.05p + 150 - 0.06p = 140 \quad\Longrightarrow\quad -0.01p = -10 \]

\[ p = \text{Rs. } 1000 \]

Checking: Rs. 50 from the 5% part and Rs. 90 from the Rs. 1500 at 6%.

Answer: A

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Find the original rate first.

\[ \text{SI} = 2600 - 2000 = 600 \quad\Longrightarrow\quad 600 = \frac{2000 \times R \times 5}{100} = 100R \]

\[ R = 6\% \]

At \( 6 + 3 = 9\% \):

\[ \text{SI} = \frac{2000 \times 9 \times 5}{100} = 900 \quad\Longrightarrow\quad \text{amount} = \text{Rs. } 2900 \]

The extra 3% over 5 years adds \( 2000 \times 0.15 = 300 \) - the same answer in one step.

Answer: C

Present worth is the sum that would grow to Rs. 132 over the two years.

\[ \text{PW}\left(1 + \frac{5 \times 2}{100}\right) = 132 \]

\[ 1.1 \times \text{PW} = 132 \quad\Longrightarrow\quad \text{PW} = \text{Rs. } 120 \]

Taking 10% off Rs. 132 would give Rs. 118.80 - the second option, and wrong, because the interest accrues on the present worth, not on the future amount.

Answer: D

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The Rs. 8470 is the amount, which is the principal plus nine years of interest.

\[ 8470 = P\left(1 + \frac{6 \times 9}{100}\right) = P(1.54) \]

\[ P = \frac{8470}{1.54} = \text{Rs. } 5500 \]

Checking: the interest is \( 5500 \times 0.54 = 2970 \), and \( 5500 + 2970 = 8470 \).