A sum, when invested at 20% simple interest per annum, amounts to ₹2400 after 3 years. What is the simple interest (in ₹) on the same sum at the same rate in 2 year?

Correct option is D

Given:

Simple Interest Rate = 20% per annum

Amount after 3 years = ₹2400

Time = 3 years

We need to find the simple interest on the same sum for 2 years at the same rate of 20%. 

Formula Used:

The formula for the amount A in simple interest is:

​$$A=P+SI$$ 

The formula for simple interest is:

​$$\text{SI} = \frac{P \times R \times T}{100}$$

where:

A = Amount after interest

P = Principal (initial sum)

SI = Simple Interest

R = Rate of interest per annum

T = Time in years 

Solution: 

​Now, we know that after 3 years, the amount is ₹2400. The simple interest formula is:

​$$\text{SI for 3 years} = \frac{P \times 20 \times 3}{100} = \frac{60P}{100} = 0.6P$$​​

The amount after 3 years is:

​$$A = P + 0.6P = 1.6P$$ 

So,  $$1.6P=2400$$​​ 

$$P = \frac{2400}{1.6} = 1500$$ 

​Thus, the principal amount $P$  is ₹1500.

​Now, we need to calculate the simple interest for 2 years using the same principal $P=1500$ and the same rate of 20%.

$$\text{SI for 2 years} = \frac{P \times R \times T}{100} = \frac{1500 \times 20 \times 2}{100}$$

$$\text{SI for 2 years} = \frac{1500 \times 40}{100} = \frac{60000}{100} = 600$$ 

​​Thus, the simple interest for 2 years is ₹600.