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?
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.
1 answers
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 $(= 8 + \frac{6}{9} = 8\frac{2}{3}minutes)$