The difference between the simple and the compound interest on a certain sum of money for 3 years at 10% p.a is Rs. 77.50. Find the sum.

Correct option is D

Given:
Difference (CI - SI) = Rs. 77.50
Time = 3 years
Rate (R) = 10% p.a.
Formula Used:
For 3 years, the difference between CI and SI is given by:
​$$D = P × (\frac{R}{100})^2 × (3 + \frac{R}{100})$$​​
Solution:
Substitute the given values into the formula:
​$$77.50 = P × (\frac{10}{100})^2 × (3 + \frac{10}{100})$$​​
​$$77.50 = P × (0.1)^2 × (3 + 0.1)$$​​
77.50 = P × 0.01 × 3.1
77.50 = P × 0.031
​$$P = \frac{77.50}{0.031} = \frac{77500}{31} = 2500$$​​
Final Answer
So the correct answer is (d)