Question

A train moves at a speed, which is $50\%$ more than the speed of a car. Both start from the point P simultaneously and arrive at a point Q, $120$ km away from P at the same time. While on the way, however, the train lost about half an hour while taking halt at the stations. The speed of the car is

• A. $80km/hr$
• B. $90km/hr$
• C. $70km/hr$
• D. $60km/hr$

Answer 1

The correct option is A $80km/hr$

Let the speed of the car be $xkm/hr$

$\therefore$Speed of the train$=x+50\%$ of $x$

$=x+\frac{50x}{100}$

$=x+\frac{x}{2}=\frac{2x+x}{2}=\frac{3x}{2}kmphr$

$\Rightarrow \frac{2}{3x}\times 120+\frac{30}{60}=\frac{120}{x}$

$\Rightarrow \frac{2}{x}\times 40+\frac{30}{60}=\frac{120}{x}$

$\Rightarrow \frac{80}{x}+\frac{30}{60}=\frac{120}{x}$

$\Rightarrow \frac{1}{2}=\frac{120}{x}-\frac{80}{x}$

$\Rightarrow \frac{1}{2}=\frac{40}{x}$

$\therefore x=80kmphr$

Hence speed of the car is $80kmphr$