Subject: General Aptitude · Chapter: Time and Distance · Exam: · Marks: · Difficulty:
A bus left $X$ for point $Y$. Two hours later a car left point $X$ for $Y$ and arrived at $Y$ at the same time as the bus. If the car and the bus left simultaneously from the opposite ends $X$ and $Y$ towards each other, they would meet $1 \frac{1}{3}$ hours after the start. How much time did it take the bus to travel from $X$ to $Y$ ?
(a)2 hours
(b)4 hours
(c)6 hours
(d)8 hours
Answer
Answer (as printed): B
Explanation
Let the distance between points $X$ and $Y$ be $d \mathrm{km}$. Suppose the bus takes $x$ hours to travel from $X$ to $Y$. Then, speed of bus $=\frac{d}{x}$ and speed of car $=\frac{d}{x-2}$. Now, sum of distances travelled by car and bus in $1 \frac{1}{3} \mathrm{hrs}$ i.e. $\frac{4}{3} \mathrm{hrs}=d$ $$\begin{aligned} & \Rightarrow\left(\frac{d}{x} \times \frac{4}{3}\right)+\left(\frac{d}{x-2} \times \frac{4}{3}\right)=d \\ & \Rightarrow \frac{4}{3 x}+\frac{4}{3(x-2)}=1 \end{aligned}$$ ∴ Required time $=4$ hours.