Raj has Rs. 1612 with him. He divided it amongst his sons Varun and Ashish and asked them to invest it at 8% rate of interest compounded annually. It was seen that Varun and Ashish got same amount after 18 and 19 years respectively. How much (in Rs. ) did Raj give to Varun?

Correct option is C

Given:
Total Amount = Rs. 1612
Rate of Interest (R) = 8% per annum compounded annually
Time: Varun = 18 years, Ashish = 19 years
Both received equal amounts after their respective durations.
Formula Used:
Compound Amount (A) = P × (1 + R/100)^T
Solution:
If Amount of Varun = Amount of Ashish, then:
​$$V × (1.08)^{18} = A × (1.08)^{19}\\=> V = 1.08 × A$$​​
Let amount given to Varun be V and to Ashish be R.
From above: => V = 1.08 × A
Total amount: A + V = 1612
=> A +1.08A = 1612
=> 2.08A = 1612
=> A = $$\frac {1612}{2.08}$$​ = Rs. 775
=> V = 1612 - 775 = Rs. 837
Therefore, Raj gave Rs. 837 to Varun.