A sum, when invested at 10% simple interest per annum, amounts to ₹3840 after 2 years. What is the simple interest (in ₹) on the same sum at the same rate of interest in 1 year?

Correct option is D

Given:

Amount after 2 years = ₹3840

Rate of interest (R) = 10% per annum

Time (T) = 2 years

Required: Simple Interest for 1 year on the same principal at the same rate

Formula Used:

Simple Interest (SI) =$$\frac{P \times R \times T}{100}$$​​

Amount (A) = P + SI

Solution:
Let’s first find SI for 2 years:

Let Principal = P

Then,

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

Substitute values:

3840 = P $$+ \frac{P \times 10 \times 2}{100} = P + \frac{20P}{100} = P(1 + 0.2) = 1.2P$$​

P $$= \frac{3840}{1.2} =$$​ ₹3200

SI for 1 year on ₹3200 at 10%:

SI $$= \frac{3200 \times 10 \times 1}{100} = ₹320$$​