Question

A sum of Rs. $18750$ is left by will by a father to be divided between two sons, $12$ and $14$ years of age, so that when they attain maturity at $18$, the amount received by each of them at $5$ per cent simple interest will be the same. Find the sum allotted at present to each son?

• A. Rs. $9500$, Rs. $9250$
• B. Rs. $8000$, Rs. $1750$
• C. Rs. $9000$, Rs. $9750$
• D. Rs. $10000$, Rs. $8750$

Answer 1

The correct option is C Rs. $9000$, Rs. $9750$

Let sum left for the $12$ years old and $14$ years old sons be Rs. $x$ and Rs. $(18750-x)$ respectively.
Then, $\frac{x\times 6\times 5}{100}+x=\frac{(18750-x)\times 4\times 5}{100}+(18750-x)$
$\Rightarrow \frac{30x}{100}+x=3750-\frac{20x}{100}+18750-x$
$\Rightarrow \frac{50x}{100}+2x=22500$

$\Rightarrow \frac{250x}{100}=22500$
$\Rightarrow x=$ Rs. $\frac{22500\times 100}{250}=$ Rs. $9000$
$\therefore$ The sum allotted to the other son is Rs. $9750$.