Manoj has Rs. 1230 with him. He divided it amongst his sons Anand and Anil and asked them to invest it at 5% rate of interest compounded annually. It was seen that Anand and Anil got same amount after 12 and 13 years respectively. How much (in Rs.) did Manoj give to Anil?

Correct option is A

Given:

Total money = Rs. 1230

Anand’s amount after 12 years = Anil’s amount after 13 years

Rate of interest = 5% p.a. compounded annually

Formula Used:

Compound Interest formula:

A = $$P \times \left(1 + \frac r{100}\right)^n$$​​

where A = Amount, P = Principal, r = Rate of interest, n = Time (years)

Solution: ​

Let Anand get P1, Anil get P2

Now, 

​$$P1\left(1 +\frac{5}{100}\right)^{12} = P2 \left(1+\frac{5}{100}\right) \\ \ \\P1 (1.05)^{12} = P2 (1.05)^{13}$$​​

P1 = 1.05 P2

Also:

P1 + P2 = 1230

1.05P2 + P2 = 1230

2.05P2 = $$\frac{1230}{2.05}$$​ = 600 

Thus, Anil gets ₹600