Question

A man allocated half of his wealth to his wife, four-fifth of the remaining to his son, two-third of the remaining to his daughter and the remaining for an endowment. If the endowment received from him was Rs. 1000 in all, his wealth was

• A. Rs. 50,000
• B. Rs. 30,000
• C. Rs. 1 lakh
• D. Rs. 10,000

Answer 1

The correct option is B Rs. 30,000

Total wealth $=x$

To his wife $=\frac{x}{2}$

To his son $=\frac{1}{2}\times \frac{4}{5}x=\frac{2x}{5}$

To his daughter $=\frac{2x}{15}$ [i.e.: $\frac{2}{3}].$

To Endowment Remaining = 1000

$\frac{x}{2}+\frac{2x}{5}+\frac{2x}{15}+1000=x$

$\frac{15x+6\left(2x\right)+2\left(2x\right)}{30}+1000=x.$

$15x+12x+4x+30000=30x$

$31x-30x=30000$

$x=30000$

$\therefore$ The wealth of person $=Rs.30000$