A person invested half of his capital at 10% simple interest and the other half at 10% compound interest (compounded annually) for 2 years. If the total interest earned is ₹ 4,100 , his total capital was

Correct option is A

Given:
Total Time (T) = 2 years
Rate (R) = 10% p.a.
Total Interest Earned = ₹4100
Formula Used:
Simple Interest =$$\frac{P × R × T}{100}$$​​
Compound Interest = $$P × (1 + \frac{R}{100})^T - P$$​​
Solution:
Let the total capital be 2P. The capital is split equally into P and P.
Simple Interest earned on first half = $$\frac{P × 10 × 2}{100}$$​ = 0.20P
Compound Interest earned on second half = $$P × (1 + \frac{10}{100})^2 - P$$​​
Compound Interest =$$P × (1.1)^2 - P = P × 1.21 - P = 0.21P$$​​
Total Interest = 0.20P + 0.21P = 0.41P
We are given that total interest is 4100.
0.41P = 4100
P =$$\frac{4100}{0.41}$$​ = 10000
Total Capital = 2P = 2 × 10000 = 20000
Final Answer
So the correct answer is (a)