Question

A mother and her two sons got a room constructed for $Rs.60,000\;$. The elder son contributes $\dfrac{3}{8}$ of his mother’s contribution while the younger son contributes $\dfrac{1}{2}$ of his mother’s share. How much do the three contribute individually?

Answer 1

Hint: Consider the mother’s contribution as $x$ and then write the contribution of her two sons in terms of her contribution which is $x$. Now add all the contributions from the mother and her two sons to get the total amount which is $Rs.60,000\;$. Find the value of $x$ on evaluating and then again substitute in the contributions of sons to get their share also.

Complete step-by-step solution:
The total amount for the construction of a room is $Rs.60,000\;$
Let’s now consider the mother’s contribution as $x$
Given that the elder son’s contribution is $\dfrac{3}{8}$ time the mother’s share.
Then the elder son’s contribution will be $\dfrac{3}{8}x$
In the same way,
Given that the younger son’s contribution is $\dfrac{1}{2}$ time the mother’s share.
Then the younger son’s contribution will be $\dfrac{1}{2}x$
Now add all the contributions from the mother and her two sons and equate it with the total amount.
$\Rightarrow x + \dfrac{1}{2}x + \dfrac{3}{8}x = Rs.60,000$
Ignore the units of money to avoid confusion.
$\Rightarrow x + \dfrac{1}{2}x + \dfrac{3}{8}x = 60,000$
Now on the LHS side, the LCM of the denominators will be $8$
$\Rightarrow \dfrac{{8x + 4x + 3x}}{8} = 60,000$
Now perform the addition operation in the numerator.
$\Rightarrow \dfrac{{15x}}{8} = 60,000$
Now multiply $8$ on both sides of the equation.
$\Rightarrow 15x = 60,000 \times 8$
Now divide $15\;$ into both sides of the equation.
$\Rightarrow x = 60,000 \times \dfrac{8}{{15}}$
On further evaluation we get,
$\Rightarrow x = 4000 \times 8$
$\Rightarrow x = 32,000$
Now substitute the value of $x$ in the contributions of the mother’s sons.
Elder sons’ contribution $\dfrac{3}{8}x = \dfrac{3}{8} \times 32000 = 12,000$
Younger son’s contribution $\dfrac{1}{2}x = \dfrac{1}{2} \times 32000 = 16,000$

$\therefore$ The mother’s contribution to the room is $Rs.32,000\;$ and her elder son’s contribution is $Rs.12,000\;$ and her younger son’s contribution is $Rs.16,000\;$.

Note: Sometimes direct fractions are given rather than the percentages of the shares. Whenever percentages are given just multiply the number with $\dfrac{1}{{100}}$ . Or to find how much percentage is the share from his mother’s contribution just multiply the fraction by a hundred.