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A local train of length 250 m should cover a distance of 100 km. There is a bridge of length ‘x’ in the journey where the maximum speed should not exceed 25 km/hr.The train used to go at a speed of 75km/hr at other places and 15 km/hr on the bridge. Due to fog, one day its speed reduced by 15 km/hr in other places. Even by travelling at 80% of the maximum speed on the bridge, it was 25 min late. How much time will the train take to cross the bridge usually (in minutes)?

A local train of length 250 m should cover a distance of 100 km. There is a bridge of length ‘x’ in the journey where the maximum speed should not exceed 25 km/hr.The train used to go at a speed of 75km/hr at other places and 15 km/hr on the bridge. Due to fog, one day its speed reduced by 15 km/hr in other places. Even by travelling at 80% of the maximum speed on the bridge, it was 25 min late. How much time will the train take to cross the bridge usually (in minutes)? Correct Answer 151

Given, length of the bridge = x

⇒ Distance need to be covered other than in the bridge = 100 - x

If the train travels in the usual speed,

Total time taken = Time taken to cross bridge + Time taken to cover remaining distance

Time = Distance/Speed

Let the total time taken by the train if it travels at usual speed be t

⇒ t = x/15 + (100 – x)/75      ----eq. 1

While the train travels in fog, it was 25 minutes late

⇒ t - 25/60 = x/20 + (100 – x)/60      ----eq. 2

Equation 1 - 2

⇒ 25/60 = x (1/15 – 1/20) +

⇒ 25/60 = x/60 – (100 – x)/300

Solving gives

 x = 37.5 km

Time taken to cross the bridge = (Length of the bridge + Length of the train)/ Speed

= (37.5 + 0.25)/15 = 37.75/15 hours

In minutes, 37.75/ 15 × 60 = 151 minutes

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