A person wants to distribute a sum of Rs. 504600 between his two sons, who are respectively 15 years and 17 years old at 5% per annum compounded annually in such a way that at the age of 22 years both receives equal amount. Find the share of elder son.

Rs. 24000

Let the share of younger son is P₁ and that of the elder son is P_2.

Time for younger son = 7 years

Time for elder son = 5 years

ATQ,

⇒ P₁(1 + \(\frac{5}{100}\))⁷ = P₂(1+\(\frac{5}{100}\))⁵

⇒ P₁(1 + \(\frac{5}{100}\))² = P₂ 

⇒ P₁(1 + \(\frac{21}{20}\))² = P₂ 

⇒ P₁ :  P₂ = 441  :  400  = 841(P)

Here,

P = P₁ +  P₂ = 841R = 504600

                           1R = 600

Share of elder son = 400R = 400 × 600 = 240000