24. A train 50 m long passes over a bridge at avelocity of 30 km/h. If

1.	24. A train 50 m long passes over a bridge at avelocity of 30 km/h. If it takes 36 s to crossthe bridge, the length of the bridge will be(a) 100 m(b) 200 m(c) 250 m (d) 300 m
Answer» Question: 24. A train 50 m long passes over a bridge at a velocity of 30 km/h. If it takes 36 s to CROSS the bridge, the LENGTH of the bridge will be (a) 100 m (b) 200 m (c) 250 m (d) 300 m Answer: (c) 250 m. Given: The length of the train is 50 m. The velocity of the train is 30 km/h. The train takes 36 seconds to cross the bridge. To find: The length of the bridge. Explanation: The velocity of the train is 30 km/h. ∴ The velocity of the train in m/s _ $(30 \times \dfrac{5}{18})\\ \\= (5 \times \dfrac{5}{3})\\ \\= (\dfrac{25}{3}) m/s$ The velocity of the train = The speed of the train = $\frac{25}{3}$ m/s. The train takes 36 seconds to cross the bridge. We know that, Speed = (DISTANCE/Time) ⇒ Distance = (Speed × Time) ⇒ Distance = ( $\frac{25}{3}$ × 36) = (25 × 12) = 300 m. ∴ Total distance covered by the train is 300 m. The length of the train is 50 m. ∴ The length of the bridge is _ (300 - 50) m = 250 m. ∴ The length of the train is 205 m. Hence, option (c) 250 m, is the correct answer.

24. A train 50 m long passes over a bridge at avelocity of 30 km/h. If it takes 36 s to crossthe bridge, the length of the bridge will be(a) 100 m(b) 200 m(c) 250 m (d) 300 m

Answer»

Question:

24. A train 50 m long passes over a bridge at a velocity of 30 km/h. If it takes 36 s to CROSS the bridge, the LENGTH of the bridge will be

(a) 100 m

(b) 200 m

(d) 300 m

Answer:

(c) 250 m.

Given:

The length of the train is 50 m.

The velocity of the train is 30 km/h.

The train takes 36 seconds to cross the bridge.

To find:

The length of the bridge.

Explanation:

The velocity of the train is 30 km/h.

∴ The velocity of the train in m/s _

$(30 \times \dfrac{5}{18})\\ \\= (5 \times \dfrac{5}{3})\\ \\= (\dfrac{25}{3}) m/s$

The velocity of the train = The speed of the train = $\frac{25}{3}$ m/s.

The train takes 36 seconds to cross the bridge.

We know that,

Speed = (DISTANCE/Time)

⇒ Distance = (Speed × Time)

⇒ Distance = ( $\frac{25}{3}$ × 36)

= (25 × 12)

= 300 m.

∴ Total distance covered by the train is 300 m.

The length of the train is 50 m.

∴ The length of the bridge is _

(300 - 50) m

= 250 m.

∴ The length of the train is 205 m.

Hence, option (c) 250 m, is the correct answer.