Question: A man can row upstream at 10 kmph and downstream at 20 kmph. Find the man's rate in still water and the rate of the stream.

Solution:

If a is rate downstream and b is rate upstream 

Rate in still water = (a + b)/2 

Rate of current = (a - b)/2 

Rate in still water = (20 + 10)/2 = 15 kmph 

Rate of current = (20 - 10)/2 = 5 kmph 

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

Question: A train 250 meters long is running at a speed of 90 km/h. How long will it take to cross a platform 150 meters long?

Solution:

speed = 90 km/h = 90 × (5/18) m/s

= 25 m/s

To cross the platform have to travel = (250 + 150) m

= 400 m

∴ Required time = 400/25 seconds

= 16 seconds