Bunuel wrote:
6. A pool has two water pumps A and B and one drain C. Pump A alone can fill the whole pool in x hours, and pump B alone can fill the whole pool in y hours. The drain can empty the whole pool in z hours, where z>x. With pumps A and B both running and the drain C unstopped till the pool is filled, which of the following represents the amount of water in terms of the fraction of the pool which pump A pumped into the pool?A. \(\frac{yz}{x+y+z}\)
B. \(\frac{yz}{yz+xz-xy}\)
C. \(\frac{yz}{yz+xz+xy}\)
D. \(\frac{xyz}{yz+xz-xy}\)
E. \(\frac{yz+xz-xy}{yz}\)
Solution: baker-s-dozen-128782-20.html#p1057508 Reading the discussion on this question made me realize how I end up retracting on the suggested strategies again and again. Since we are talking about Quant, you would expect to have a definite set of rules but no sir, you don't.
I repeat this quite often: When you have a question using variables and the answer is in terms of those variables, your life is easier than if you get a question using numbers. The reason - you can assign your own 'cool' values to the variables for which the relations hold. Then just go on and check the option which gives you the right answer.
I retract it with the following - But if the number of variables is high, say 3 or 4 or more, it might be too cumbersome to plug in values for each variable and keep in mind what stands for what. This could lead to a lot of confusion and errors.
I retract it again - But if you can give some very convenient values to the variables, go ahead and plug it in.
This question has variables and the answer is in terms of the variables so plugging in values is a good option. But the number of variables is 3 which could make it cumbersome. But, you can give the variables such values that you get your answer quickly.
I need to find the rate of A. There are no constraints on the values x, y, and z can take except z > x (drain C empties slower than pipe A fille)
Let's say, x = 4, y = 8, z = 8
What did I do here? I made the rate of B same as the rate of C. This means, whenever both of them are working together, drain C cancels out the work of pipe B. So the entire pool will be filled by pipe A and the amount of water pumped in by A will be the entire pool. Hence, if y = z, pipe A fills the entire pool i.e. the amount of water in terms of fraction of the pool pumped by A is 1.
In the options, put y = z and see which option gives you 1.
Only options (B) and (E) do.
Now let's say, x = 8, y = 4, z = 8.00001 ( z should be greater than x but let's assume it is infinitesimally greater than x such that we can approximate it to 8 only)
Rate of work of C is half the rate of work of B. Rate of work of C is same as rate of work of A. All the work done by pipe A is removed by drain C. So if pipe B fills the pool, drain C empties half of it in that time (this is the water pumped by pipe A)
Put x = z in the options B and E. You get y/z = 4/8 = 1/2 in option (B).
Answer (B)
Even if you end up feeling that this method is complicated, try and wrap your head around it. It might give you some ideas of logical solutions in some other questions.
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