Veer has Rs. 1632 with him. He divided it amongst his sons Nitin and Pravin and asked them to invest it at 4% rate of interest compounded annually. It was seen that Nitin and Pravin got same amount after 12 and 13 years respectively. How much (in Rs. ) did Veer give to Nitin?

Correct option is B

Given:

Total amount = Rs. 1632

Nitin’s investment duration = 12 years

Pravin’s investment duration = 13 years

Rate of interest = 4% p.a. (compounded annually)

Amounts received by both are equal

Formula Used:

Compound Interest based Final Amount:

A = $$P \left(1 + \frac{R}{100} \right)^T$$​​

Solution:

Let Nitin’s principal = P1, Pravin’s principal = P2 

Now, 

​$$P1\left(1 + \frac{4}{100}\right)^{12} = P2\left(1 + \frac{4}{100}\right)^{13}\\ \ \\ P1 (1.04)^{12} = P2 (1.04)^{13} \\ \ \\P1 = 1.04 \times P2$$​​

Also,

P1 + P2 = 1632

Substituting P1 = 1.04 × P2 into the total:

1.04P2 + P2 = 1632

2.04P2 = 1632

P2 = $$\frac{1632}{2.04}$$​ = 800

Nitin's principal = 1632 - 800 = ₹832