Question

if a train run at 40 kmph it reaches its destination late by 11 minutes late. but if it runs at 50kmph it late by 5 minutes only. find the distance covers by train.

Answer 1

Let the total distance to be covered by train = D km
Let the fair time would be taken by train, i.e no delay/no before = T minutes 
If speed s1 = 40km/h then 11 delay.
S₁ = 40km/h = 40 /60  = 4/6  km/min.
T₁ = T+11  minutes

If speed s2 = 50km/h then 5 min delay.
S₂ = 50km/h = 50 /60 = 5/6 km/min.
T₂ = T + 5 minutes
_______________________________________________________
A/Q,
D = S₁*T₁
d = (4/6)*(T + 11) --------------------------------(i)
D = S₂*T₂ 
d = (5/6)*(T + 5) --------------------------------(ii)
From eqns (i) & (ii)
4(T + 11)/6 = 5(T + 5)/6
⇒ 5T - 4T = 44- 25
⇒ T = 19 min
put the value of T in eqn (ii)
D = 5(19+5)/6
D = 20 km.
Therefore distance covered by train = 20 km.