Question 67

Dinesh travels 760 km to his home, partly by train and partly by car. He takes 8 hoursif he travels 160 km bytrain and the rest by car. He takes 12 minutes moreif he travels 240 km bytrain and the rest by car. The speedsof the train and the car respectively are

Solution

Let speeds of train and car be $$x$$ km/hr and $$y$$ km/hr respectively.

According to ques,

=> $$\frac{160}{x}+\frac{600}{y}=8$$ ----------(i)

and $$\frac{240}{x}+\frac{520}{y}=8+\frac{12}{60}=8.2$$  -----------(ii)

Applying : 3 x (i)-2 x (ii)

=> $$\frac{1800}{y}-\frac{1040}{y}=24-16.4$$

=> $$\frac{760}{y}=7.6$$

=> $$y=\frac{760}{7.6}=100$$

Similarly, $$x=\frac{160}{2}=80$$

$$\therefore$$ Speeds of train and car are 80 km/hr and 100 km/hr respectively.

=> Ans - (A)


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