1

Question

An express train takes 1hour less than a passenger train to travel 132 Km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of Express train is 1 Km/h more than that of the passenger train, find the average speeds of the train.

Open in App

Solution

● A correction in your question. Average speed of express train is 11km/hr more than passenger train.

○ Solution:-

Let,

average speed of the passenger train be 'x' km/hr

the average speed of the express train be (x + 11) km/hr

Distance between Mysore and Bangalore = 132 km

It is given that the time taken by the express train to cover the distance of 132 km is 1 hour less than the passenger train to cover the same distance.

So,

time taken by passenger train = 132/x hr

The time taken by the express train = {(132)/x+11} hr

Now, according to the question

{132/(x+11)} = 132/x + 1

[ After taking L.C.M. of 132/x +1 and then solving it we get (132+x)/x. ]

{132/(x+11)} = (132+x)/x

By cross multiplying, we get,

132x = x²+132x+11x+1452

x² + 11x - 1452 = 0

x² + 44x - 33x - 1452 = 0

x(x+44) - 33(x+44) = 0

(x+33) (x+44) = 0

x - 44 or x = 33

As the speed cannot be in negative

therefore, x = 33

◎ the speed of the passenger train = 33km/hr

◎ speed of express train is 33 + 11 = 44 km/hr

○ Solution:-

Let,

average speed of the passenger train be 'x' km/hr

the average speed of the express train be (x + 11) km/hr

Distance between Mysore and Bangalore = 132 km

It is given that the time taken by the express train to cover the distance of 132 km is 1 hour less than the passenger train to cover the same distance.

So,

time taken by passenger train = 132/x hr

The time taken by the express train = {(132)/x+11} hr

Now, according to the question

{132/(x+11)} = 132/x + 1

[ After taking L.C.M. of 132/x +1 and then solving it we get (132+x)/x. ]

{132/(x+11)} = (132+x)/x

By cross multiplying, we get,

132x = x²+132x+11x+1452

x² + 11x - 1452 = 0

x² + 44x - 33x - 1452 = 0

x(x+44) - 33(x+44) = 0

(x+33) (x+44) = 0

x - 44 or x = 33

As the speed cannot be in negative

therefore, x = 33

◎ the speed of the passenger train = 33km/hr

◎ speed of express train is 33 + 11 = 44 km/hr

3

Join BYJU'S Learning Program

Join BYJU'S Learning Program