Rs. 21750 is invested by a person in the bank account of his two sons whose ages are 9 years and 13 years in such a way that they will get equal amount at an age of 21 years at the rate of 4.5% per annum. Find the share of younger son.

10200

Let the share of younger son = P₁

                share of elder son = P₂

Time for younger son = 21 - 9 = 12

Time for elder son = 21 - 13 = 8

effective R% for younger son = 12 × 4.5% = 54%

effective R% for elder son = 8 × 4.5% = 36%

P₁ × \(\frac{154}{100}\) = P₂ × \(\frac{136}{100}\)

\(\frac{P_1}{P_2}\) = \(\frac{136}{154}\) = \(\frac{68}{77}\)

       P₁           P₂ 

       68          77          =     145

        ↓                                   ↓

      × 150                           × 150

        ↓                                   ↓

   10,200                           21,750