Question

A factory was owned by three people $X,Y$ and $Z$, each having an equal share. $X$ sold half his share to $Y.Z$ sold one quarter of his share to $Y$. What fraction did $Y$ then own?

• A. $\frac{5}{12}$
• B. $\frac{1}{12}$
• C. $\frac{7}{12}$
• D. None of these

Answer 1

Answer: (C)

$\frac{7}{12}$

According to the question, $x,y$ and $z$ has $\frac{1}{3}$ share each.

According to the question,

$X$ sold $\frac{1}{2}$ of $\frac{1}{3}$to $Y$

$\Rightarrow \frac{1}{6}$ to $Y$

$Z$ sold $\frac{1}{4}$ of $\frac{1}{3}$ to $Y$

$\Rightarrow \frac{1}{12}$ to $Y$

Now $Y$ share $=$ $\frac{1}{3}+\frac{1}{6}+\frac{1}{12}=\frac{7}{12}$