Question

A sum, when invested at 10% simple interest per annum, amounts to ₹4560 after 2 years. What is the simple interest (in ₹) on the same sum at the same rate of interest in 1 year?

• A. 1520
• B. 380
• C. 190
• D. 760

Answer 1

Answer:

B. 380

To find the simple interest for one year, we first need to determine the original principal amount.

Step 1: Find the Principal Amount ($P$)

We are given:

• Rate ($R$): $10\%$ per annum

• Time ($T$): $2$ years

• Amount ($A$): $₹4560$ (Principal + Interest for 2 years)

The formula for Amount in Simple Interest is:

$A = P + \frac{P \times R \times T}{100}$

Substituting the values:
$4560 = P + \frac{P \times 10 \times 2}{100}$

$4560 = P + 0.2P$

$4560 = 1.2P$

$P = \frac{4560}{1.2} = \mathbf{3800}$

Step 2: Calculate Simple Interest for 1 year

Now, we find the interest on $₹3800$ at $10\%$ for $1$ year:
$\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}$

$\text{SI} = \frac{3800 \times 10 \times 1}{100}$

$\text{SI} = \mathbf{380}$

The simple interest on the same sum for one year is ₹380.