Rishi has Rs. 1612 with him. He divided it amongst his sons Shan and Piyush and asked them to invest it at 8% rate of interest compounded annually. It was seen that Shan and Piyush got same amount after 19 and 20 years respectively. How much (in Rs. ) did Rishi give to Shan?

Correct option is B

Given:
Total money = Rs. 1612
Shan’s investment time = 19 years
Piyush’s investment time = 20 years
Rate of interest = 8% compounded annually
Both received the same amount at the end
Formula Used:
​$$A = P \left(1 + \dfrac{R}{100}\right)^T$$​​
Where:
• A = Amount after time T
• P = Principal
• R = Rate of interest
• T = Time
Solution:
Let the amounts invested be:
Shan = x
Piyush = 1612 - x
Amount after 19 years for Shan = $$x × (1.08)^{19}$$​​
Amount after 20 years for Piyush = $$(1612 - x) × (1.08)^{20}$$​​
Since both amounts are equal:
​$$x × (1.08)^{19 }= (1612 - x) × (1.08)^{20}$$​​
x = (1612 - x) × 1.08
x = 1740. 96- 1.08x
x + 1.08x = 1740.96
2.08x = 1740.96
x  = 837 
Rishi gave Rs. 837 to Shan.