A sum, when invested at 20% simple interest per annum, amounts to ₹2160 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:

Amount after 3 years = ₹2160

Rate of simple interest = 20% per annum

Time = 3 years (for the given amount)

Formula Used:

Amount (A) = Principal (P) + Simple Interest (SI)

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

Where:

P = Principal

R= Annual rate of interest (in percentage)

T = Time in years

​Solution:

Let the principal be P.

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

Amount after 3 years = P + SI = P + 0.6P = 1.6P

Given that the amount is ₹2160, we have 1.6P = ₹2160

Therefore, P = $$\frac{ ₹2160 }{ 1.6 }$$ = ₹1350

SI for 2 years =$$\frac{P \times R \times T}{100} = \frac{1350 \times 20 \times 2}{100} = ₹540$$

Option (D) is right.