A sum of Rs. 18750 is left by a will by a father to be divided between the two sons, 12 and 14 years of age, so that when they attain maturity at 18, the amount (principal + interest) received by each at 5 percent simple interest will be the same. Find the sum alloted at present to each son.

A. Rs. 9500, Rs. 9250 B. Rs. 8000, Rs. 1750 C. Rs. 9000, Rs. 9750 D. None of these Answer: Option C
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Solution(By Apex Team)

Let the two sums be Rs. x and Rs. (18750 – x). Then, $\begin{array}{l}=x+\frac{x\times5\times6}{100}=(18750-x)+\frac{(18750-x)\times5\times4}{100}\\ \Leftrightarrow x+\frac{30x}{100}=(18750-x)+3750-\frac{20x}{100}\\ \Leftrightarrow2x+\frac{x}{2}=22500\\ \Leftrightarrow\frac{5x}{2}=22500\\ \Leftrightarrow x=\left(\frac{22500\times2}{5}\right)\\ \Leftrightarrow x=9000\end{array}$ So the other sum will be = ( 18750 – 9000) = 9750 Hence, The two sums are Rs. 9000, Rs. 9750