1.

If two pipes P and Q are such that, they can fill a large tub in 6 and 18 minutes respectively. They are opened on alternate minutes. Find in how many minutes, the tub shall be full?1). 6 min.2). 10 min.3). 18 min.4). 24 min.

Answer»

TIME-taken by PIPE P to fill the tub = 6 mins

∴ Part of tub filled by Pipe P in one minute = 1/6

Time-taken by pipe Q to fill the tub = 18 min.

∴ Part filled by Pipe Q in one minute = 1/18

The part of tank filled in a span of 2 minutes $(= \;\frac{1}{6} + \frac{1}{{18}} = \frac{4}{{18}} = \frac{2}{9})$

∴ part of tub filled in 8 minutes $(= \;4\; \times \frac{2}{9}\; = \frac{8}{9})$

⇒ Part of tub left to be filled = 1 – (8/9) = 1/9

After 8 minutes, it’s pipe A’s turn to fill the tub and 1/9th part of the tub is empty.

Pipe A fills the entire tub in 6 minutes, so the time taken by pipe A to fill 1/9th of tub = 6/9 min.

⇒ Total time taken $(= 8 + \frac{6}{9} = 8\frac{2}{3}minutes)$



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