Raj has Rs. 1218 with him. He divided it amongst his sons Varun and Ashish and asked them to invest it at 10% rate of interest compounded annually. It was seen that Varun and Ashish got same amount after 13 and 14 years respectively. How much (in Rs. ) did Raj give to Ashish?

Correct option is D

Given:

Total amount = Rs. 1218

Interest rate = 10% compounded annually

Varun gets amount after 13 years

Ashish gets amount after 14 years

Final amounts for both are equal

Formula Used:

Compound interest formula:

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

Solution:​

Let Varun’s principal = ₹V and Ashish’s principal = ₹A

V + A = ₹1218

Since both final amounts are equal:

​$$V \times (1.10)^{13} = A \times (1.10)^{14} \\ \ \\ \implies V = (1.10) \times A$$​​

Substitute ( V = 1.10A ) into the total:

1.10A + A = 1218

2.10A = 1218

A = $$\frac{1218}{2.10}$$​ = ₹580

Thus, ₹580 was given to Ashish