Pipes A and B can fill a tank with water in 30 minutes and 40 minutes,…

2025

Pipes A and B can fill a tank with water in 30 minutes and 40 minutes, respectively, while pipe C can drain off 51 litres of water per minute. If all the three pipes are opened together, the tank is filled in 90 minutes. What is the capacity (in litres) of the tank?

  1. A.

    900

  2. B.

    864

  3. C.

    720

  4. D.

    1080

Attempted by 25 students.

Show answer & explanation

Correct answer: D

Solution:

Let x be the capacity of the tank in litres.

  1. Rates: Pipe A fills at x/30 litres per minute, Pipe B fills at x/40 litres per minute, Pipe C drains 51 litres per minute. Net filling rate = x/30 + x/40 - 51.

  2. All three open together fill the tank in 90 minutes, so 90 × (x/30 + x/40 - 51) = x.

  3. Compute x/30 + x/40 = (4x + 3x)/120 = 7x/120. Substitute: 90 × (7x/120 - 51) = x.

  4. Simplify: 90 × 7x/120 = (90/120) × 7x = (3/4) × 7x = 21x/4. Also 90 × 51 = 4590. So 21x/4 - 4590 = x.

  5. Rearrange: 21x/4 - x = 4590 ⇒ (21/4 - 4/4)x = 4590 ⇒ 17x/4 = 4590 ⇒ x = 4590 × 4/17 = 1080.

Answer: The capacity of the tank is 1080 litres.

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