**Quote:**

I'm doubting if the ratios are correct. trying to figure out how the ratios are seted up, the problem says " P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it." or P=(3/4)xQ => P:Q = 3:4 not 4:3 as stated above in red. same thing for the other ratio P=(2/3)xR => P:R = 2:3

now if we even out P to be 6 ( for 2 and 3) we get P:Q:R = 6:8:9 and Q part will be 8/(8+6+9) = 8/23 which is not correct answer.

Am I missing something or what is wrong here, what do you think

Bunuel and

sandeep1756Hi

kzivrev,

The question gives us the ratio of time taken by Pipes P, Q and R to do a particular work i.e. draining the tank. We know from the time work equation that

Work = Rate * Time. So

rate is inversely proportional to the time taken.

So if the time taken are in the ratio of 2:1 the rates will be in the ratio of 1:2. For example if John can make 6 sandwiches in an hour and Mike can make 6 sandwiches in half an hour the ratio of time taken by John and Mike is 2:1 and hence the ratio of their rates would be 1:2 i.e Mike can make sandwiches twice as fast as John.Coming back to the question, if all the 3 pipes work simultaneously, they would be working for the same amount of time.Hence

to find the proportion of work done by pipe Q we need to find the ratios of rates of pipes P, Q and R.

Since the ratio of time taken by pipes P & Q to do a particular work is 3:4, the ratio of their rates would be 4:3. On the same lines, if the ratio of time taken by pipes P & R to do a particular work is 2:3, the ratio of their rates would be 3:2.

Hence if we assume the rate of pipe P as \(x\), we can write the rate of pipe Q as \(\frac{3x}{4}\) and rate of pipe R as \(\frac{2x}{3}\). The proportion of work done by pipe Q can be calculated as rate of pipe Q divided by the total rates of pipe P, Q and R.

The sum of the rates of pipes P, Q and R is \(\frac{29x}{12}\). Hence the proportion of work done by pipe Q would be \(\frac{3x * 12}{4 * 29x} = \frac{9}{29}\).

Hope its clear

Regards

Harsh

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