Subject: General Aptitude · Chapter: Time and Distance · Exam: 2006 · Marks: · Difficulty:
A train $M$ leaves station $X$ at 5 a.m and reaches station $Y$ at 9 a.m. Another train $N$ leaves station $Y$ at 7 a.m. and reaches station $X$ at 10.30 a.m. At what time do the two trains cross each other?
(a)7.36 a.m
(b)7.56 a.m
(c)8.36 a.m
(d)8.56 a.m
Answer
Answer (as printed): B
Explanation
Let the distance between stations $X$ and $Y$ be $x \mathrm{km}$ and let the trains meet $y$ hours after 7 a.m. Clearly, M covers $x \mathrm{km}$ in 4 hrs and $N$ covers $x \mathrm{km}$ in (7/2) hrs. $$\therefore \quad \text { Speed of } M=\frac{x}{4} \mathrm{kmph}, \text { Speed of } N=\frac{2 x}{7} \mathrm{kmph} .$$ Distance covered by $M$ in $(y+2)$ hrs + Distance covered by $N$ in $y \mathrm{hrs}=x$. $$\begin{aligned} & \therefore \quad \frac{x}{4}(y+2)+\frac{2 x}{7} \times y=x \Leftrightarrow \frac{(y+2)}{4}+\frac{2 y}{7}=1 \\ & \Leftrightarrow \quad y=\frac{14}{15} \mathrm{hrs}=\left(\frac{14}{15} \times 60\right) \mathrm{min} .=56 \mathrm{min} . \end{aligned}$$ Hence, the trains meet at 7.56 a.m.