Ashish has ₹1,218 with him. He divides it amongst his sons Arun and Mahesh and asks them to invest it at 10% rate of interest compounded annually. It was seen that Arun and Mahesh got same amount after 11 and 12 years, respectively. How much (in ₹) did Ashish give to Mahesh?​

Correct option is B

Given:
Ashish has ₹1,218.
He divides this amount between his sons, Arun and Mahesh, and asks them to invest it at 10% interest compounded annually.
Arun's investment is for 11 years, and Mahesh's investment is for 12 years.
Both Arun and Mahesh end up with the same amount after their respective investment periods.
Formula Used:
​$$A = P \left( 1 + \frac{r}{100} \right)^t$$​​
Where:
A = Amount after t years
P = Principal amount (initial investment)
r = Annual interest rate
t = Time in years
Solution:
Let the amount given to Arun be x and the amount given to Mahesh be 1,218 - x.
Since the amounts are equal:
​$$x \times (1.1)^{11} = (1,218 - x) \times (1.1)^{12}\\x = (1,218 - x) \times 1.1\\x = 1,218 \times 1.1 - x \times 1.1\\x = 1,339.8 - 1.1x\\x + 1.1x = 1,339.8\\\\2.1x = 1,339.8\\x = \frac{1,339.8}{2.1} = 638\\$$​​
So, Ashish gave Arun ₹638. Therefore, Ashish gave Mahesh: 1,218 - 638 = 580