Time and Work

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A bath can be filled by the cold water pipe in 10 min and by hot water pipe in 15 min (independently each). A person leaves the bathroom after turning on both pipes simultaneously and returns at the moments when the bath should be full. Finding, however, that the waste pipe has been open he now closes it. In 4 min more, bath is full. In what time would be the waste pipe empty it?


9 min


12 min


15 min


14 min

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Option(A) is correct

Let us assume some time l.c.m(10, 15)min=30 min

Now in 30 min time cold water pipe will fill the bath \(\dfrac{30}{10}=3\) times whereas hot water pipe will fill it  \(\dfrac{30}{15}=2\) times.

So in 30 min time bath will be filled $3+2=5$ times.

So emptied bath will be fully filled in \(\dfrac{30}{5}=6\) min time if waste pipe is closed.

Initially waste pipe is opened, after 6 mins is passed and waste pipe is closed it takes 4 more minutes to fill the bath fully.

So waste pipe has emptied the \(\dfrac{4}{6}=\dfrac{2}{3}\)part of bath in 6 mins.

Rest \(\dfrac{1}{3}\)part of tank can be emptied by the waste pipe in \(\dfrac{6}{2}=3 \) mins.

So waste pipe would empty the tank in 6+3=9 mins

Edit: For an alternative solution using Unitary Method, check comment by Chirag Goyal.

(11) Comment(s)


one can see in simple way-

6 min it takes if both pipes are filing. OK

Suppose T=0 at the start of all the process. When he checked the bath it was not filled and it took 4 min to fill. But in 6 min it should be filled if waste was not opened.

now very important statement-

Hence after 6min work left was equal to 4min of filling pipe. which is equal to 6 min of empty tank.


6min to fill without a waste pipe.

4 min extra time to fill with closed a waste pipe.

in 6 min w.pipe did work is 6/x to do same work for cold and hot pipe takes 4min.



by solving for x,

x=9 min.

this is so simple if you understand this....


it's a wrong solution. Nowhere in the question, it is mentioned that waste time opens after the tank is full. So how can we conclude that it worked for 6 minutes?


It's not wrong, as it is mentioned in the question, WASTE PIPE WAS OPEN SINCE THE START.

To the second part of your question, in order to conclude that it worked for 6 minutes, we need to do calculations based on the data given in the question.

Chirag Goyal

Had the Waste pipe not been open, Both Pipe would fill the tub in

$T\left(\dfrac{1}{10}+\dfrac{1}{15}\right)=1$ $Unitary\ Method$

$\text{T = 6 min}$

Due to Leak whole process takes $\bf{6+4=10\ min}$

this means that Both Hot & Cold Water Pipe fills together for $\text{10 min}$ But Waste Pipe kept emptying for first $\text{6 min}$ only.

Now Waste Pipe would empty full Tub in $W\ min(say)$

Then final Equation Should be

$10\left(\dfrac{1}{10}+\dfrac{1}{15}\right) -\dfrac{6}{W}=1$

$\text{W = 9 min}$ is the required Answer.


how come $9$ mins not $90$ mins, i may be terribly wrong.. plz explain

Mousumi Roy

talented banda hai!!


Can it be done in any alternative way? Like in one minute,


Is it a correct equation?

The Flash

It certainly can be solved using 1 min. But, I believe the equation you wrote is incorrect.

Poonam Pipaliya

how 4/6 came...???...!!!


As tank should have been filled in 6 mins had waste pipe been closed. Now when waste pipe is closed it takes 4 more min to fill the tank. In these 4 min, with waste pipe closed, tank is filled completely.

So this is the amount of water which was emptied by waste tank which is $\frac{4}{6}=\frac{2}{3}$ parts.

Hope that helps.