Two pipes A & B can fill a tank in 8 min & 12 min respectively. Both the pipes are opened together but after 3 min, pipe A is turned off. What is the remaining time required to fill the tank?

Question

Question

This question was previously asked in

HPCL Engineer Civil 23 Dec 2023 Official Paper

Answer 1

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Given:

Two pipes A & B can fill a tank in 8 min & 12 min respectively. Both the pipes are opened together but after 3 min, pipe A is turned off.

Concept:

To find the total time required to fill the tank using the rates of flow of each pipe.

Formula Used:

Rate of pipe A = 1/8 tank/min

Rate of pipe B = 1/12 tank/min

Calculation:

We have,

⇒ Rate of pipe A = 1/8 tank/min

⇒ Rate of pipe B = 1/12 tank/min

Both pipes are opened together for 3 minutes:

⇒ Part filled by A in 3 min = 3 × (1/8) = 3/8

⇒ Part filled by B in 3 min = 3 × (1/12) = 3/12 = 1/4

⇒ Total part filled in 3 min = 3/8 + 1/4

⇒ Total part filled in 3 min = 3/8 + 2/8 = 5/8

Remaining part to be filled by pipe B = 1 - 5/8

⇒ Remaining part = 3/8

Time taken by pipe B to fill 3/8 of the tank = (3/8) / (1/12)

⇒ Time = 3/8 × 12/1 = 36/8 = 4.5 min

Hence, the total time required to fill the tank is 4.5 minutes.