A boat of a length 500 m passes a Ghat along the Ganga River in 30 seconds when it is moving downstream and while in return it passes the same Ghat in 45 seconds. Find the length of the Ghat if the speed of the current is 10 m/s.

A boat of a length 500 m passes a Ghat along the Ganga River in 30 seconds when it is moving downstream and while in return it passes the same Ghat in 45 seconds. Find the length of the Ghat if the speed of the current is 10 m/s. Correct Answer 1300 m

Short Trick:

Let speed of the boat be u m/s.

⇒ (u + 10) 30 = (u -10) 45

⇒ u = 50 m/s

⇒ Length of ghat = {(50 + 10) × 30} - 500 = 1300 m

Detailed Solution:

Let speed of the boat be x m/s and the length of the Ghat be y m.

⇒ Distance covered by boat = length of the Ghat + length of the boat

= y + 500

⇒ Time taken by boat in downstream = 30 sec

⇒ (y + 500) / (x + 10) = 30

⇒ 30(x + 10) = y + 500

⇒ 30x + 300 = y + 500

⇒ 30x = 200 + y

⇒ x = (200 + y) /30      ----(1)

Now,

⇒ Time taken by boat in upstream = 45 sec

⇒ (y + 500) / (x - 10) = 45

⇒ 45(x - 10) = y + 500

Using equation (1), we get

⇒ 45 = y + 500

⇒ 1.5(200 + y) = 950 + y

⇒ 300 + 1.5y = 950 + y

⇒ 0.5y = 650

⇒ y = 1300

∴ Length of the Ghat is 1300m