Question

A man divides his property so that his son's share to his wife's and the wife's share to his daughter are both in the ratio $3:1$. If the daughter gets $10,000$ less than the son, find the total worth of the property.

• A. $15,000$
• B. $16,250$
• C. $20,000$
• D. $25,000$

Answer 1

The correct option is B $16,250$

The ratio of son and wife is son:wife $=3:1$ or we can write it as $9:3$.

The ratio of wife and daughter is wife:daughter $=3:1$

Therefore, the ratio of son, wife and daughter is:

Son:wife:daughter $=9:3:1$

Sum of the ratios $=9+3+1=13$

Let the total wealth be Rs. $x$, then

Son's share- daughter's share =Rs. $10,000$ that is:

$\frac{9x}{13}-\frac{x}{13}=10000\Rightarrow \frac{9x-x}{13}=10000\Rightarrow \frac{8x}{13}=10000\Rightarrow 8x=130000\Rightarrow x=\frac{130000}{8}\Rightarrow x=16250$

hence, the total worth of the property is Rs. $16,250$.