A sum of ₹ 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 per cent simple interest will be the same. Find the sum allotted at present to each son.
(a)₹ 9500, ₹ 9250
(b)₹ 8000, ₹ 1750
(c)₹ 9000, ₹ 9750
(d)None of these
Answer
Answer (as printed): C
Explanation
Let the two sums be ₹ $x$ and ₹ ( $18750-x$ ). Then, $\quad x+\frac{x \times 5 \times 6}{100}=(18750-x)+\frac{(18750-x) \times 5 \times 4}{100}$ $$\begin{aligned} & \Leftrightarrow \quad x+\frac{30 x}{100}=(18750-x)+3750-\frac{20 x}{100} \\ & \Leftrightarrow \quad 2 x+\frac{x}{2}=22500 \Leftrightarrow \frac{5 x}{2}=22500 \\ & \Leftrightarrow \quad x=\left(\frac{22500 \times 2}{5}\right)=9000 . \end{aligned}$$ Hence, the two sums are ₹ 9000 and ₹ 9750.
Explanation as extracted from the printed page; notation may be imperfect.