Raj has ₹1,218 with him. He divided it amongst his sons Varun and Ashish and asked them to invest it at 10% rate of interest per annum, compounded annually. It was seen that Varun and Ashish got the same amount after 13 and 14 years, respectively. How much (in ₹) did Raj give to Ashish?​

Correct option is A

Given:

Raj has ₹1,218, which he divides between his sons Varun and Ashish.

The interest rate is 10% per annum, compounded annually.

Varun invested his amount for 13 years and Ashish for 14 years.

Formula Used:

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

Solution:

Let the amount Raj gave to Varun be x and the amount Raj gave to Ashish be y.

Now, From the condition;

$$x \left(1 + \frac{10}{100}\right)^{13} = y \left(1 + \frac{10}{100}\right)^{14}$$​​

​$$\frac{x}{y} = 1 + \frac{10}{100}$$​​

​$$\frac{x}{y} = \frac{110}{100}$$​​

​$$\frac {x}{y} = \frac{11}{10}$$​​

Now, x = 11 unit and y = 10 unit 

Ashish gets = $$\frac{1218}{21}\times 10 = ₹580$$​​

Thus, Raj gave ₹580 to Ashish.