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 16 and 17 years respectively. How much (in Rs. ) did Ashok give to Raj?

Correct option is A

Given:
Total amount = Rs. 1612
Rate of interest = 8% per annum
Time = 16 years and 17 years
Formula Used:
​$$A = P (1 + \frac{R}{100})^T$$​​
Solution:
Let Raj’s share = x
Varun’s share = 1612 − x
​$$x(1.08)^16 = (1612 − x)(1.08)^17 \\\ \\\text {Dividing both sides by} (1.08)^16:x = (1612 − x) × 1.08\\\ \\x = 1740.96 − 1.08x\\\ \\2.08x = 1740.96\\\ \\x ≈ 837\\\ \\$$​​