Ashok has Rs. 1612 with him. He divided it amongst his sons Raj and Varun and asked them to invest it at 8% rate of interest compounded annually. It was seen that Raj and Varun got same amount after 15 and 16 years respectively. How much (in Rs. ) did Ashok give to Raj?

Correct option is B

Given:
Total amount with Ashok = Rs. 1612
Raj invested for 15 years
Varun invested for 16 years
Rate of interest = 8% compounded annually
Both received the same final amount
Concept Used:
$$A = P \left(1 + \frac{R}{100} \right)^T$$ 
Solution:
Let Raj’s principal = R and Varun’s principal = V
Since both received the same amount:$$R(1.08)^{15} = V(1.08)^{16} \Rightarrow R = 1.08V$$

$$R(1.08)^{15} = V(1.08)^{16} \Rightarrow R = 1.08V$$​​
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From the total amount: R + V = 1612
Substitute R = 1.08V into the equation:
1.08V + V = 1612
2.08V = 1612
V = 1612 ÷ 2.08 = 775
R = 1.08 × 775 = 837
Raj got 837 as its share