Simple Interest Questions and Answers

Answer: A

The amount is Rs. 1,380.

\[ \begin{aligned} \text{SI} &= \frac{1200 \times 5 \times 3}{100} = 180 \\ \text{Amount} &= 1200 + 180 = 1380 \end{aligned} \]

Rs. 1,260 would be the amount after one year only, and Rs. 1,290 and Rs. 1,240 do not match 5% simple interest for three years. Rs. 1,470 comes from a much higher rate.

Simple interest is earned only on the original principal, so it is the same Rs. 60 in each of the three years.

Answer: C

The rate of interest was 10% p.a.

Using \(\text{SI} = \frac{P \times R \times T}{100}\):

\[ \begin{aligned} R &= \frac{100 \times \text{SI}}{P \times T} \\ &= \frac{100 \times 1500}{5000 \times 3} = 10 \end{aligned} \]

Check: 10% of Rs. 5,000 is Rs. 500 a year, and three years give Rs. 1,500. At 8%, 9% or 11% the interest would be Rs. 1,200, Rs. 1,350 or Rs. 1,650.

The formula rearranges as \(R = \frac{100 \times \text{SI}}{P \times T}\), so the rate can be read off directly once the interest, principal and time are known.

Answer: B

The rate is 8% per annum.

Simple interest is \(SI = \frac{P \times R \times T}{100}\). Here \(SI = \frac{2}{5}P\) and \(T = 5\) years.

\[ \begin{aligned} \tfrac{2}{5}P &= \frac{P \times R \times 5}{100} \\ R &= \frac{2}{5} \times \frac{100}{5} \\ &= 8 \end{aligned} \]

Check: at 8% for 5 years the interest is 40% of the sum, which is \(\frac{2}{5}\). 10% would give half the sum, and 6% gives 30%.

Answer: B

The interest is ₹ 1,200.

Simple interest is principal times rate times time, divided by 100:

\[ SI = \frac{5000 \times 8 \times 3}{100} = 1200 \]

So the interest after 3 years is ₹ 1,200. Each year earns ₹ 400 (8% of 5,000), and three years earn three times that.

₹ 1,000 and ₹ 1,400 do not match any whole number of years at ₹ 400 a year, and ₹ 1,800 would need 4.5 years.

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 \( 5500 + 2970 = 8470 \).

Answer: A

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

Becoming \( \tfrac{7}{6} \) of itself means the interest is \( \tfrac{1}{6} \) of the principal.

\[ \frac{P}{6} = \frac{P \times R \times 3}{100} \]

\[ \frac{1}{6} = \frac{3R}{100} \quad\Longrightarrow\quad R = \frac{100}{18} = \frac{50}{9} = 5\tfrac{5}{9}\% \]

The multiple applies to the amount, so subtracting 1 gives the interest as a fraction of the sum.