Algebra - Pipes and Cistern pblm

to fill half tank it will take 6 hrs and 10 hrs to empty it.
Take LCM of it i.e. 60
consider work is 60
filling work done per hr 60/6= 10
emptying work done per hr 60/10= 6

one tap is filling and another is emptying so work= 10-6 =4
4 work is done per hr.
to complete the work i.e. 60 it will take 60/4 hrs = 15 hrs

Hello Saurabh,

This is a fairly simple question on Rates. As such, it’s imperative that you work on this by trying to find out the individual rates of the two pipes which are doing the work.

In this case, the work to be done by the pipes can be assumed to be the capacity of the tank.

The filling tap can fill an empty tank in 12 hours. The emptying tap can empty half the tank in 10 hours – what does this mean? It only means that the emptying tap can empty the whole tank in 20 hours. Makes sense?

So we have the respective times taken by the two taps – 12 hours and 20 hours. Therefore, let’s assume the work to be done (i.e. capacity of the tank) to be the LCM of these two numbers.

The LCM of 12 and 20 is 60. So, let capacity of tank = 60 litres.

What does this mean now? This means that the filling tap can fill 60 litres in 12 hours, right? That essentially means that it fills the tank at the rate of 5 litres per hour.

Similarly, the emptying tap, which is able to empty 60 litres in 20 hours, empties the tank at the rate of -3 litres per hour (negative rate since it empties the tank).

Now, if both are opened simultaneously, effective work done by both = 5 -3 = 2 litres per hour. At this rate, to fill half the tank i.e. 30 litres, the two taps will have to work for a total of 15 hours.

The correct answer option is B.

It’s interesting to note that this question only has 4 answer options, which should only make your job easier than on a GMAT type of question.

On questions related to Rates (Time & Work), always use the LCM method to assume the work done and proceed to find out the rates and the times. This is, by far, the fastest approach in most Rates problems that you see on the GMAT.

Also, be careful about the traps laid out for you in Rates questions. For example, here, at the fag end of the question, the question suddenly changes flavor and asks you to find the time taken by both taps to fill HALF the tank. Many students fall for this trap, because, in the flow of solving questions, they end up making the mistake of not reading the entire question carefully, and solve the question assuming the question is asking them to find the time taken to fill the whole tank.

See how the trap answer sits at the top, as option A?? Low hanging fruit, isn’t it?


Hope that helps!