Question

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

• A. 80 km/hr, 100 km/hr
• B. 100 km/hr, 80 km/hr
• C. 120 km/hr, 100 km/hr
• D. 100 km/hr, 120 km/hr

Answer 1

The Correct Option is A

Assume the speed of train be \(x\ \frac{km}{hr}\)

Assume the speed of car be \(y\ \frac{km}{hr}\)

From the question, we know that

= \(\frac{160}{x} + \frac{600}{y} = 8\)  – equation (i)

= \(\frac{240}{x} + \frac{520}{y} = 8 + \frac{12}{60} = 8.2\)  – equation (ii)

Multiplying equation (i) by 3 and equation (ii) by 2 we get,

\(\frac{1800}{y} - \frac{1040}{y} = 24 - 16.4\)

\(\frac{720}{y} = 7.6\)

\(y = \frac{760}{7.6}\)

= 100

\(x = \frac{160}{2} = 80\)

So, the speed of train is \(80\ \frac{km}{hr}\)

the speed of car is\(100\ \frac{km}{hr}\)

The correct option is (A): 80 km/hr, 100 km/hr