Question

Mohan 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. the speed of the train and the car, respectively are: (a) 80 km/h, 100 km/h (b) 100 km/h, 80 km/h (c) 120 km/h, 120 km/h (d) 100 km/h, 120 km/h (e) none of these

Answer 1

Take the speed of train as x kmph and car be y kmph
Condition(i):
Given that Mohan travelled a distance of 760 km
Distance travelled by train = 160 km
Recall, time taken = distance / speed
Hence time taken to travel by train = 160/x
Distance travelled by car = 600 km
Time taken to travel by car = 600/y
Total time taken = 8 hours

Condition (ii):
Distance travelled by train = 240 m
Time taken to travel by train = 240 / x
Distance travelled by car = 760 - 240 = 520 km
Time taken to travell by car = 520 / y
Total time taken = 8 hrs + 12 minutes
                         = 8 + (12/60)
                         = 8.2 hours

Hence equations (1) and (2) becomes

Put y = 100 in (1), we get

Thus speed of train is 300 kmph and speed of car is 100 kmph.