Pipe A, B and C can fill a cistern in 12, 24, 48 hrs respectively. If all the pipes are opened simultaneously, Find the time when the pipe… — Answer & Discussion

Pipe A, B and C can fill a cistern in 12, 24, 48 hrs respectively. If all the pipes are opened simultaneously, Find the time when the pipe B must be turned off, so that the cistern may be just filled in 8 hrs?

A5 hrs
B4 hrs
C6 hrs
D3 hrs

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Discussion 1

CCommunity11 Jul 2019

Total units of water to be filled in the cistern = LCM of (12, 24, 48) = 48 units

⇒ Pipe A can fill 4 units of water in 1 hr.

⇒ Pipe B can fill 2 units of water in 1 hr.

⇒ Pipe C can fill 1 unit of water in 1 hr.

Let pipe B is closed after x hrs.

But, A and C pipes remained on for 8 hrs

We can write,

8 × 4 + 2x + 8 × 1 = 48

= 32 + 2x + 8 = 48

⇒ 2x = 8

⇒ x = 4 hrs

∴ pipe B is closed after 4 hrs so that cistern is just filled in 8 hrs.