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?

Given:

Principal (P) = ₹1218

Rate (r) = 10%

Time for Arun (t₁) = 11 years

Time for Mahesh (t₂) = 12 years

Amount received by Arun = Amount received by Mahesh

Formula used:

A = P × (1 + r/100)^t

Calculations:

Let the amount given to Arun be ₹x and to Mahesh be ₹(1218 - x).

For Arun:

A = x × (1 + 10/100)¹¹

For Mahesh:

A = (1218 - x) × (1 + 10/100)¹²

Since both amounts are equal:

x × (1.1)¹¹ = (1218 - x) × (1.1)¹²

⇒ x × (1.1)¹¹ = (1218 - x) × (1.1 × (1.1)¹¹)

⇒ x = (1218 - x) × 1.1

⇒ x = 1218 × 1.1 - x × 1.1

⇒ x + 1.1x = 1218 × 1.1

⇒ 2.1x = 1218 × 1.1

⇒ x = (1218 × 1.1) / 2.1

⇒ x = ₹638

∴ Amount given to Mahesh = 1218 - x = ₹1218 - ₹638 = ₹580

The correct answer is option (2).