Mahesh travels 250 km to his home partly by train and partly by bus. He takes 6 hours if he travels 50 km by train and remaining distance by bus. If he travels 100 km by train and remaining distance by bus, he takes 7 hours. Find the speed of the train and the bus separately.

Let the speed of the train and the bus be x km/hr and y km/hr respectively.

We know that

Total distance travelled by Mahesh = 250 km

In the first case it is given that he travels 50 km by train and 200 km by bus.

Given that total time taken by Mahesh to reach in this case = 6 hr

In the second case it is given that he travels 100 km by train and 150 km by bus.

Given that total time taken by Mahesh to reach in this case = 7 hr

Putting these value in above equations, we get

50a + 200b = 6 … (i), 100a + 150b = 7 ….. (ii)

So, the given equations transforms into linear equation in two variables.

Multiply equation (i) by 2,

100a + 400b = 12 … (iii)

100a + 150b = 7 ….. (ii)

Subtract (ii) from (iii),

100a + 400b – 100a – 150b = 12 – 7

⇒ 250b = 5

Putting above value in (ii),