A train running at 48 km/h crosses a man going with the speed of 12 km/h, in the same direction, in 18 seconds and passes a woman coming from the opposite direction in 12 seconds. The speed (in km/h) of the woman is :

6

Relative speed = 48 - 12 = 36 km/h

(When both moves in same direction )

36 km/h = 36 × \(\frac{5}{18}\) =  10 m/sec

Distance = Speed × Time

= 10 × 18 = 180 m

Now ,

In 2 nd case

Let speed of woman = x km/h

Relative speed = (x + 48) km/h

Time taken to cross each  other = 12 sec

Relative Speed  = \(\frac{180}{12}\) = 15 m/sec

15 m /sec = 15 × \(\frac{18}{5}\) = 54 km/h

Now , x + 48 = 54 km/h

x = 6 km/h

So speed of women = 6 km/h