Mahesh has ₹1617 with him. He divided it amongst his sons Vijay and Ajay and asked them to invest it at 10% rate of interest compounded annually. It was seen that Vijay and Ajay got same amount after 13 and 14 years respectively. How much (in ₹) did Mahesh give to Vijay?

Given:

Amount Mahesh has = ₹1617

Rate of interest = 10% per annum, compounded annually

Vijay's time period = 13 years, Ajay's time period = 14 years

Vijay and Ajay received the same amount after 13 and 14 years, respectively.

Formula used:

The compound interest formula is:

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

A = Amount after time t

P = Principal

r = Rate of interest

t = Time period

Calculations:

Let the amount Mahesh gave to Vijay be ₹x and to Ajay be ₹(1617 - x).

According to the given condition, Vijay and Ajay received the same amount after 13 and 14 years, so we can write the equation for their amounts:

x(1 + 10/100)¹³ = (1617 - x)(1 + 10/100)¹⁴

⇒ x(1.1)¹³ = (1617 - x)(1.1)¹⁴

Divide both sides by (1.1)¹³:

⇒ x = (1617 - x)(1.1)

⇒ x = 1617 × 1.1 - x × 1.1

⇒ x + x × 1.1 = 1617 × 1.1

⇒ x(1 + 1.1) = 1617 × 1.1

⇒ x × 2.1 = 1617 × 1.1

⇒ x = (1617 × 1.1) / 2.1

⇒ x = 1778.7 / 2.1

⇒ x = ₹846.43 ≈ ₹847

Therefore, Mahesh gave ₹847 to Vijay.