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.

1Rs. 9500, Rs. 9250
2Rs. 8000, Rs. 1750
3Rs. 9000, Rs. 9750
4None of these

Answer:- 1

Explanation:-

Solution:

Let the two sums be Rs. x and Rs. (18750 - x).
Then,

\begin{aligned} = x + \frac{x \times 5 \times 6}{100} = (18750 - x) + \frac{(18750 - x) \times 5 \times 4}{100} \\ \Leftrightarrow x + \frac{30 x}{100} = (18750 - x) + 3750 - \frac{20 x}{100} \\ \Leftrightarrow 2 x + \frac{x}{2} = 22500 \\ \Leftrightarrow \frac{5 x}{2} = 22500 \\ \Leftrightarrow x = (\frac{22500 \times 2}{5}) \\ = 9000. \end{aligned}

$\eqalign{ & = x + \frac{{x \times 5 \times 6}}{{100}} = \left( {{\text{18750}} - x} \right) + \frac{{\left( {{\text{18750}} - x} \right) \times 5 \times 4}}{{100}} \cr & \Leftrightarrow x + \frac{{30x}}{{100}} = \left( {{\text{18750}} - x} \right) + 3750 - \frac{{20x}}{{100}} \cr & \Leftrightarrow 2x + \frac{x}{2} = 22500 \cr & \Leftrightarrow \frac{{5x}}{2} = 22500 \cr & \Leftrightarrow x = \left( {\frac{{22500 \times 2}}{5}} \right) \cr & = 9000. \cr}$
Hence,
The two sums are Rs. 9000, Rs. 9750