Correct Answer - Option 1 : 20 sec
Given:
Speed of train to cross a bridge = x m/sec
Time taken by train to cross the bridge with speed of x m/s = 60 sec
Speed of train to cross the pole = 2x m/sec
Time taken by train to cross the pole with the speed of 2x m/s = 8 sec
Length of bridge = 660 m
Formula used:
Time = Distance/Speed
Concept used:
If a train crosses a bridge or any other horizontal object, distance travelled by train would be the sum of length of the bridge and the length of the train
If any train crosses a man/pole or any other vertical object, distance travelled by train is equal to length of the train
Calculations:
Distance travelled by train to cross the pole = 2x × 8 = 16x
length of train = 16x
Distance travelled by train to cross the bridge = 60 × x = 60x
⇒ 60x = 660 + 16x
⇒ 44x = 660
⇒ x = 15 m/sec
Length of train = 16 × 15 = 240 m
Now, speed of train = 3x = 3 × 15 = 45 m/sec
Time taken to cross the bridge = (660 + 240) /45 = 20 sec
∴ Time taken to cross the bridge with the speed 3x m/s is 20 sec