A person wants to distribute a sum of Rs. 390300 between his two sons, who are respectively 13 years and 15 years old at 4% per annum compounded annually in such a way that at the age of 18 years both receives equal amount. Find the share of younger son.

Rs. 187500

Let the share of younger son P₁ and elder son is P₂

Time for younger son = 5 years

Time for elder son = 3 years

ATQ,

⇒  P₁(1 + \(\frac{4}{100}\))⁵ = P₂(1+\(\frac{4}{100}\))³

⇒  P₁(1 + \(\frac{4}{100}\))² = P₂ 

⇒  P₁(1 + \(\frac{26}{25}\))² = P₂ 

Hence,

    P₁     :      P₂      ⇒    P

  625     :     676    ⇒  1301

⇒ P = 1301R = 390300

⇒  1R = 300

⇒ Share of younger son (P₁) =  625R = 625 × 300 = 1,87,500