Question

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in.
(a) 81 min
(b) 108 min
(c) 144 min
(d) 192 min

Answer 1

Hint: We will take \[x\] minutes as the time taken by the slower pipe to fill the tank. A faster pipe will fill the tank in \[\dfrac{x}{3}\] minutes. Using these information and further details we will solve this question by using a unitary method.

Complete step-by-step answer:
Let the time taken by the slower pipe to fill the tank be \[x\] minutes and let the time taken by the faster pipe to fill the tank be \[\dfrac{x}{3}\] minutes.
Part of the tank filled by slower pipe in 1 minute \[=\dfrac{1}{x}........(1)\]
Part of the tank filled by faster pipe in 1 minute \[=\dfrac{3}{x}........(2)\]
It is mentioned in the question that together the two pipes can fill the tank in 36 minutes. So using this information we add up equation (1) and equation (2) and then equate it to \[\dfrac{1}{36}\] because this is the part of the tank which is filled by both pipes in 1 minute.
 \[\,\Rightarrow \dfrac{1}{x}+\dfrac{3}{x}=\dfrac{1}{36}........(3)\]
Now rearranging equation (3) we get,
 \[\,\Rightarrow \dfrac{4}{x}=\dfrac{1}{36}........(4)\]
Cross multiplying equation (4) and then solving for x we get,
 \[\,\Rightarrow x=4\times 36=144\]
Hence the slower pipe will alone be able to fill the tank in 144 minutes. And hence option (c) is the correct answer.

Note: Whatever the question is asking us to find we will take it to be x, this way it consumes less time. We may get confused in finding the part of the tank filled in 1 minute but here the unitary method comes into play. It is given in the question that the faster pipe fills the tank 3 times faster than the slower pipe so we in a hurry may think that faster pipe takes 3x minutes to fill the pipe.