Question

$A$ and $B$ walk from $X$ to $Y$, a distance of $27$ km, at $5$ km/hr and $7$ km/hr, respectively. $B$ reaches $Y$ and immediately turns back meeting $A$ to $Z$. What is the distance from $X$ to $Z$?

• A. $22.5$ km
• B. $20.0$ km
• C. $25.0$ km
• D. $24.5$ km

Answer 1

The correct option is A $22.5$ km

Time taken by $A$ in covering $(27-x)$ km is the same as time taken by $B$ in covering $(27+x)$ km
Therefore, $\frac{27-x}{5}=\frac{27+x}{7}$

$\Rightarrow 189-7x=135+5x$

$\Rightarrow 12x=54$

$\Rightarrow x=\frac{54}{12}=\frac{27}{6}km$
Thus $XZ=27-\frac{27}{6}=27\times \frac{5}{6}=22.5$ km