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.

Solution(By Examveda Team)

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