Each inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours. When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened. After how many hours will the cistern be completely filled?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 26 Jul 2023 Shift 2)

Answer 1

Given:

Each inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours.

When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day

Calculation:

Let total work is 420 units ( LCM of 84 and105 and)

The efficiency of 1 inlet pipe = 420 /84

⇒ 5 units

The efficiency of 1 out let pipe= 420 / 105

⇒ 4 units

The efficiency of 9 inlet pipes = 9 × 5

⇒ 45 units

The efficiency of 10 outlet pipes = 10 × 4

⇒ 40 units

Total efficiency of is (45 - 40) / = 5 units

The time will be 420 / 5 = 84 hrs

∴ The correct option is 1

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