Question

Question 122
A mother and her two daughters got a room constructed for Rs. 62000. The elder daughter contributes $\frac{3}{8}$ of her mother's contribution while the younger daughter contributes $\frac{1}{2}$ of her mother's share. How much do the three contribute individually?

Answer 1

Let the mother's share be Rs. x
Now, elder daughter's share $=Rs.\frac{3}{8}x$
and younger daughter's share $=Rs.\frac{1}{2}x$
According to the question,
$x+\frac{3}{8}x+\frac{x}{2}=62000$
$\Rightarrow \frac{8x+3x+4x}{8}=62000\Rightarrow 15x=62000\times 8\Rightarrow x=\frac{62000\times 8}{15}\Rightarrow x=\frac{12400\times 8}{3}\Rightarrow x=\frac{99200}{3}=33066.6$
So, mother's share = Rs. 33066.6
Elder daughter's share $=\frac{3}{8}\times \frac{99200}{3}=Rs.12400$
Younger daughter's share $=\frac{1}{2}\times \frac{99200}{3}=Rs.16533.3$
Hence, mother and her two daughters contributed Rs. 33066.6, Rs. 12400 and Rs. 16533.3 respectively.