Question

Shubham travels 760 km to his home partly by train and partly by Car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and the rest by car. Find the speed of the train and car respectively (in km/hr).

• A. $40,80$
• B. $60,120$
• C. $80,100$
• D. $100,120$

Answer 1

The correct option is C $80,100$

Let speed of train be t and that of car be c.
Now, case I,
$\frac{160}{t}+\frac{600}{c}=8$
Case II,
$\frac{240}{t}+\frac{520}{c}=\frac{41}{5}$
Multiply equation (1) by 3 and equation (2) by 2 an subtract,
$\frac{480}{t}+\frac{1800}{c}-\frac{480}{t}-\frac{1040}{c}=24-\frac{82}{5}$
$\frac{760}{c}=\frac{38}{5}$
$c=\frac{760\times 5}{38}$
$c100$ km/hr
Put this value in equation 1,
$\frac{160}{t}+\frac{600}{100}=8$
$t=80$ km/hr
Thus, speed of car $=100km/hr$ and speed of train $=80km/hr.$