Ashish has ₹1617 with him. He divided it amongst his sons Arun and Mahesh and asked them to invest it at 10% rate of interest compounded annually. It was seen that Arun and Mahesh got same amount after 14 and 15 years respectively. How much (in ₹) did Ashish give to Arun?

Given:

Ashish has ₹1617, divided between Arun and Mahesh.

Rate of interest (r) = 10% compounded annually.

Time for Arun (t_Arun) = 14 years.

Time for Mahesh (t_Mahesh) = 15 years.

After the respective times, Arun and Mahesh have the same amount.

Formula used:

A = P(1 + r/100)^t

Where:

• A = Final amount
• P = Principal amount
• t = Time in years
• r = Rate of interest

Calculations:

Let the amount given to Arun = ₹P_Arun and to Mahesh = ₹P_Mahesh.

It is given that the final amounts are the same after respective times.

⇒ P_Arun(1 + 10/100)¹⁴ = P_Mahesh(1 + 10/100)¹⁵

⇒ P_Arun(1.1)¹⁴ = P_Mahesh(1.1)¹⁵

⇒ P_Arun = P_Mahesh × (1.1)

Total amount distributed:

P_Arun + P_Mahesh = ₹1617

Substitute P_Arun = P_Mahesh × 1.1:

⇒ P_Mahesh × 1.1 + P_Mahesh = ₹1617

⇒ P_Mahesh(1.1 + 1) = ₹1617

⇒ P_Mahesh(2.1) = ₹1617

⇒ P_Mahesh = ₹1617 / 2.1

⇒ P_Mahesh = ₹770

Now, calculate P_Arun:

⇒ P_Arun = P_Mahesh × 1.1

⇒ P_Arun = ₹770 × 1.1

⇒ P_Arun = ₹847

∴ The correct answer is option (3): ₹847.