Rafique and Pritam invested identical sums of money for two years at interest rates that compound annually at 15% per annum and 10% per annum respectively. If Rafique earns ₹2,250 more as interest than Pritam during these two years, then how much did each of them invest initially?

Correct option is B

Given:
Rafique and Pritam invested identical sums of money for 2 years.
Rafique's investment earns 15% per annum compounded annually.
Pritam's investment earns 10% per annum compounded annually.
Rafique earns ₹2,250 more as interest than Pritam during these two years.
We need to find the initial amount invested by each of them.
Formula Used:
Compound Interest Formula:
A =$$P \left(1 + \frac{r}{100}\right)^t$$​​
where:
A = Amount after t years
P = Principal amount

r = Annual interest rate
t  = Time in years
The interest earned is:
$$\text{Interest} = A - P$$​
Solution:
Let the initial investment be  P .
Both Rafique and Pritam invested the same amount  P .
Calculate the amount for Rafique after 2 years
Rafique's interest rate = 15% per annum.
​$$A_{\text{Rafique}} = P \left(1 + \frac{15}{100}\right)^2 = P (1.15)^2 = P \times 1.3225$$​​
Interest earned by Rafique:
​$$\text{Interest}_{\text{Rafique}} = A_{\text{Rafique}} - P = 1.3225P - P = 0.3225P$$​​
Pritam's interest rate = 10% per annum.
​$$A_{\text{Pritam}} = P \left(1 + \frac{10}{100}\right)^2 = P (1.10)^2 = P \times 1.21$$​​
Interest earned by Pritam:
​$$\text{Interest}_{\text{Pritam}} = A_{\text{Pritam}} - P = 1.21P - P = 0.21P$$​​
Rafique earns ₹2,250 more as interest than Pritam:
​$$\text{Interest}_{\text{Rafique}} - \text{Interest}_{\text{Pritam}} = 2,250$$​​
0.3225P - 0.21P = 2,250
0.1125P = 2,250
P$$= \frac{2,250}{0.1125} = 20,000$$​
Each of them initially invested ₹20,000.

Alternate Method:
Let the initial investment be P .
Calculate the difference in interest earned:
$$P \left(1.15^2 - 1\right) - P \left(1.10^2 - 1\right) = 2,250$$​​
P (1.3225 - 1) - P (1.21 - 1) = 2,250
P (0.3225) - P (0.21) = 2,250
0.1125P = 2,250
P =$$\frac{2,250}{0.1125} = 20,000$$​​
Thus, each of them initially invested ₹20,000.