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A and B together can fill a tank in 12 mins, B and C together can fill the tank in 15 mins and C and A can fill a tank in 20 mins. In how much time will B take to fill the tank ?

A and B together can fill a tank in 12 mins, B and C together can fill the tank in 15 mins and C and A can fill a tank in 20 mins. In how much time will B take to fill the tank ? Correct Answer 20 min.

Given:

Time taken by A + B = 12 mins

Time taken by B + C = 15 mins

Time taken by C + A = 20 mins

Formula  used:

Total work = Efficiency × Number of days

Calculation:

L.C.M of (12, 15 and 20) = 60 = Total work

⇒ Efficiency of  (A + B) = 60/12 = 5 units

⇒ Efficiency of (B + C) = 60/15 = 4 units

⇒ Efficiency of (C + A) =60/20 = 3 units

⇒ Total eff. 2(A + B + C) = 12 unit

⇒ (A + B + C) = 6 unit 

⇒ Efficiency of B = Efficiency of (A + B + C) – Efficiency of (A + C)

⇒ Efficiency of C = 6 – 3 = 3 units

⇒ Time taken by B to fill the tank = 60/3

⇒ 20 mins

∴ B will take 20 mins to fill the tank

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