A sum, when invested at 10% simple interest per annum, amounts to ₹2880 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 B

Given:

Amount after 2 years = ₹2880

Rate of interest = 10% per annum

Time = 2 years

We need to find the simple interest (SI) for 1 year.

Formula Used:

Simple Interest (SI) $$=\frac{P \times R \times T}{100}$$​​
Where:
P = Principal,
R = Rate of interest per annum,
T = Time in years.

The formula for the amount A after time T is:

A = P+ SI

Solution:

We are given the amount after 2 years (₹2880), so:

2880 = P + SI for 2 years

SI for 2 years is:

SI for 2 years =$$\frac{P \times R \times T}{100} = \frac{P \times 10 \times 2}{100} = \frac{20P}{100} = \frac{P}{5}$$​

Substituting this into the amount formula:

2880 = P + $$\frac{P}{5}$$​​

2880 =$$\frac{6P}{5}$$​

14400 = 6P

P = $$\frac{14400}{6} =$$​ 2400
Now that we know the principal P = 2400, we can calculate the simple interest for 1 year:

SI for 1 year =$$\frac{P \times R \times T}{100} = \frac{2400 \times 10 \times 1}{100} = \frac{24000}{100}$$​ = 240

The simple interest for 1 year is ₹240.