Discussion

Question:

Two pipes A & B can fill a cistern in 16 and 24 minutes respectively. If both the pipes are opened simultaneously, then after how much time should B be closed so that the tank is filled in 12 minutes?

Explanation:

Let B closed after x mins, then part filled by (A + B) in x mins + part filled by A in (12 - x) mins = 1]

∴ $x (\frac{1}{16} + \frac{1}{24}) + (12 - x) \frac{1}{16} = 1$ or $\frac{5 x}{48} + \frac{12 - x}{16} = 1$

⇒ 5x + 36 - 3x = 48

⇒ 2x = 12 ⇒ x = 6

So, B must be closed after 6 mins.

Hence, option (b).

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