Subject: General Aptitude · Chapter: Time and Distance · Exam: 2003 · Marks: · Difficulty:
A train can travel 50\% faster than a car. Both start from point $A$ at the same time and reach point $B$ 75 kms away from $A$ at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is
(a)100 kmph
(b)110 kmph
(c)120 kmph
(d)130 kmph
Answer
Answer (as printed): C
Explanation
Let speed of the car be $x \mathrm{kmph}$. Then, speed of the train $=\frac{150}{100} x=\left(\frac{3}{2} x\right) \mathrm{kmph}$. $$\begin{aligned} \therefore \frac{75}{x}-\frac{75}{\frac{3}{2} x} & =\frac{125}{10 \times 60} \Leftrightarrow \frac{75}{x}-\frac{50}{x} \\ & =\frac{5}{24} \Leftrightarrow x=\left(\frac{25 \times 24}{5}\right)=120 \mathrm{kmph} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.