Question

Rahul travels $600$ km to his home partly by train and partly by car. He takes 8 hours if he travels $120$ km by train and the rest by car. He takes $20$ minutes longer if he travels $200$ km by train and the rest by car. Find the speed of the train and the car.

• A. Speed of train $=20$km/h & Speed of car $=40$ km/hr
• B. Speed of train $=60$ km/h & Speed of car $=80$ km/hr
• C. Speed of train $=45$ km/h & Speed of car $=52$ km/hr
• D. Speed of train $=66$ km/h & Speed of car $=88$ km/hr

Answer 1

Answer: (B)

Speed of train $=60$ km/h & Speed of car $=80$ km/hr

Let the speed of train $=x$ km/hr
The speed of car $=y$ km/hr
$\because$ time $=$ distance/speed

According to the 1st condition

Time taken to cover $120$ km by train $+$ time taken to cover

$480$ km by car $=8$ hrs

$\Rightarrow \frac{120}{x}+\frac{480}{y}=8$ ....(1)

According to the $2^{nd}$ condition, we have
Time taken to cover $200$ km by train $+$ time taken to cover $400$ km by car $=8$ hrs $20$ min

$\Rightarrow \frac{200}{x}+\frac{400}{y}=\frac{25}{3}$ ....(2)

$[8$ hrs $20$ min $=(8+\frac{20}{3})hrs=\frac{25}{3}]$

Multiply equation (1) by $200$ and equation (2) by $120$ and subtract both.

$\Rightarrow (\frac{24000}{x}+\frac{96000}{y}=1600)-(\frac{24000}{x}+\frac{48000}{y}=1000)$

$\Rightarrow \frac{48000}{y}=600$

$\Rightarrow y=80$

Put $y=80$ in equation (1),

$\Rightarrow \frac{120}{x}+\frac{480}{80}=8$

$\Rightarrow \frac{120}{x}=2$

$\Rightarrow x=60$

Hence, the speed of train $=60$ km/hr.
The speed of car $=80$ km/hr.