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The tank will get filled by four A, B, C and D inlets. By A, B and D, tank will get filled in 5 minutes. By A and C inlets, tank will get filled in 20/3 minutes. Through B, C and D inlets, tank will filled in 20/3 minutes. In how much time 3/4th of tank will get filled when all four inlets are opened?

The tank will get filled by four A, B, C and D inlets. By A, B and D, tank will get filled in 5 minutes. By A and C inlets, tank will get filled in 20/3 minutes. Through B, C and D inlets, tank will filled in 20/3 minutes. In how much time 3/4th of tank will get filled when all four inlets are opened? Correct Answer 3 minutes

Calculation:

⇒ 1/A + 1/B + 1/D = 1/5

⇒ 1/A + 1/C = 3/20

⇒ 1/B + 1/C + 1/D = 3/20

Adding all equations,

⇒ 2/A + 2/B + 2/C + 2/D = 1/5 + 3/20 + 3/20 = 1/2

⇒ 2(1/A + 1/B + 1/C + 1/D) = 1/2

⇒ (1/A + 1/B + 1/C + 1/D) = 1/4

Tank will filled in 4 minutes by 4 inlets.

∴ 3/4th tank will be filled in = 3/4 × 4 = 3 minutes.

Important Points

Fraction of tank to be filled × 1/(pipe's 1 hour's work) = Total time in which fraction of work filled

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