Discussion
A divided Rs. 25,500 between his two grandsons, 13-year-old P and 14-year-old Q, in such a way that each would receive the same amount on turning 25. Until then the money stays in a bank earning 4% compounded annually. How much of it was Q's share?
Answer: B
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
P is 13 and so waits 12 years; Q is 14 and waits 11. Both end with the same amount:
\[ P_{\text{share}}(1.04)^{12} = Q_{\text{share}}(1.04)^{11} \]
\[ Q_{\text{share}} = P_{\text{share}} \times 1.04 \]
The younger boy's money compounds for an extra year, so he needs less of it. Their shares are therefore in the ratio \( 25 : 26 \):
\[ P_{\text{share}} + 1.04\,P_{\text{share}} = 25500 \quad\Longrightarrow\quad 2.04\,P_{\text{share}} = 25500 \]
\[ P_{\text{share}} = 12{,}500, \qquad Q_{\text{share}} = \text{Rs. } 13{,}000 \]
Checking: \( 12500 \times 1.04 = 13000 \), so after Q's extra year the two balances coincide.
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