Question

A railway engine travels with a speed of 90km/h. The decrease in its speed is directly proportional to the square root of the number of Wagons attached to it. If 25 wagons attached, it can run at a speed of 60 km/h. What is the number of wagons attached to the engine if it runs at a speed of 54 km/h? *​

Answer 1

Solution :-

Given that, decrease in speed of train is directly proportional to the square root of the number of Wagons attached to it.

So,

→ Decrease in speed ∝ √(No. of wagons.)

→ Dec. in speed = k * √n [ k is constant term here and n = No. of wagons.)

Now, given that,

→ speed of Train engine = 90km/h . (Mean with 0 wagons .)

→ when 25 wagons attached , speed becomes = 60km/h.

So, we can say that,

→ Because of 25 wagons speed is decreased by = 90 - 60 = 30 km/h.

A/q,

→ Dec. in speed = k * √n

→ 30 = k * √25

→ 30 = k * 5

→ k = 6.

Therefore, when speed is 54 km/h , speed is decreased by = 90 - 54 = 36 km/h.

So,

→ Dec. in speed = k * √n

→ 36 = 6 * √n

→ 6 = √n

→ n = 36 wagons (Ans.)

Hence, when trains runs at a speed of 54km/h , 36 wagons are attached to it.