Question: The ratio between the speeds of two trains is 5 : 8. If the second train runs 600 km in 5 hours, then the speed of the first train is -

Solution:

Let the speed of the trains are 5x and 8x

the speed of the second train = 600/5 kmph = 120 kmph

∴ 8x = 120

x = 15

∴ speed of first train = 5x = 75 kmph

Question: An aeroplane covers a certain distance at a speed of 250 kmph in 6 hours. To cover the same distance in 100 minutes, it must travel at a speed of-

Solution: 

Total Distance = (250 × 6) = 1500 km. 

Time 100 minutes = 100/60 hr 

= 5/3 hr 

We know that, 

Speed = Distance/Time

∴ Required speed = 1500/(5/3) km/hr 

= 900 km/hr.

Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is-

Solution: 

Let the length of the train is x m and speed is s.

ATQ,

s = (x + 800)/100 and,

s = (x + 400)/60

∴ (x + 800)/100 = (x + 400)/60

or, 60x + 48000 = 100x + 40000

or, 40x = 8000

or, x = 200 m