Question

A mother and her two daughters got a room constructed for $₹62,000$ . The elder daughter contributes $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ of her mother’s contribution while the younger daughter contributes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ of her mother’s share. How much do the three contribute individually?

Answer 1

A mother and her two daughters got a room constructed for $₹62,000$

The elder daughter’s contributions $\raisebox{1ex}{$=3$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ of her mother’s share

The younger daughter’s contributions $=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ of her mother’s share

Let us assume the mother’s share be $S$,

The elder daughter’s contributions $=\frac{3}{8}S$

The younger daughter’s contributions $=\frac{1}{2}S$

So, mother’s share $+$ elder daughter’s share $+$ younger daughter’s share $=₹62,000$

$S+\frac{3}{8}S+\frac{1}{2}S=₹62,000$

Taking the LCM of the denominators $1,8$ and $2$ which is $8$, we get:

$$\begin{gathered} \frac{8S+3S+4S}{8}=₹62,000 \\ \frac{15}{8}S=₹62,000 \\ S=\frac{₹62,000\times 8}{15} \\ S=\frac{₹496000}{15} \\ S=₹33,066.6 \end{gathered}$$

∴ Mother’s share $=₹33,066.6$

Elder daughter’s share $=\frac{3}{8}S=\frac{3}{8}\times ₹33,066.6=₹12,400$

Younger daughter’s share $=\frac{1}{2}S=\frac{1}{2}\times ₹33,066.6=₹16,533.3$

∴ The individual share of the three members are

∴ Mother’s share $=₹33,066.6$

Elder daughter’s share $=₹12,400$

Younger daughter’s share $=₹16,533.3$