Anand has Rs. 1612 with him. He divided it amongst his sons Anil and Ashok and asked them to invest it at 8% rate of interest compounded annually. It was seen that Anil and Ashok got same amount after 11 and 12 years respectively. How much (in Rs.) did Anand give to Anil?

Correct option is A

Given:
Total = 1612, rate = 8% p.a., amounts after 11 and 12 years are equal. 
Formula Used:
For compound interest maturity: Amount = $$P \times (1 + r)^n$$​​
Solution:  
Let Anil = P₁, Ashok = P₂

$$A_1 = A_2\\\ \\P_1(1.08)^{11} = P_2(1.08)^{12}\\\ \\P_2 = \frac{P_1}{1.08}\\\ \\Also,\\\ \\P_1 + P_2 = 1612\\\ \\P_2 = \frac{P_1}{1.08} = P_1 \times \frac{25}{27}\\\ \\P_1 + P_1\left(\frac{25}{27}\right) = 1612\\\ \\P_1 \left(1 + \frac{25}{27}\right) = 1612\\\ \\P_1 \left(\frac{52}{27}\right) = 1612\\\ \\P_1 = 1612 \times \frac{27}{52}\\\ \\P_1 = \left(\frac{1612}{52}\right) \times 27 = 31 \times 27 = 837\\\ \\$$​​
So Anil got Rs. 837.