# P is able to do a work in 15 days and Q the same work in 10 days. If they work together for 2 days, how much work left?

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P is able to do a piece of work in 15 days and Q can do the same work in 10 days. If they can work together for 2 days, what is the fraction of work left?

posted Apr 7, 2017

I think it would be 2/3 since:

``````1 - ((2/15) + (2/10)) = 1 - ((4/30) + (6/30)) = 1 - (10/30) = 1 - 1/3 = 2/3
``````
answer Apr 8, 2017 by anonymous

There is a simple trick here to solve problems on work and time faster
First we have to take the LCM of the days both people take to complete a piece of work ie., LCM of 15,10 = 30.
Now this leads to 2 ratios 30/15 = 2 and 30/10 = 3 which represents thier work speed (higher = faster) also 30 represents the total work that needs to be done.

So for this problem both of them are working together for 2 days. So thier speed = 3+2 = 5/day. Therefore total work done after 2 days = 10, which is 1/3rd of the total work done. So the amount work left to be done = 2/3rd.

Its given that p does a work in 15 days, it means that P completes (1/15) of the work in each day.
Similarly, it's also given that q does a work in 10 days which means that q completes (1/10) of the work in each day .
Now, p and q are working together for 2 days then:-
1) p completes 2*(1/15) of the work in two days
2) q completes 2*(1/10) of the work in two days
Therefore on adding 2/15 and 2/10 we get 1/3
So one third of the work is completed which implies two third of the work is remaining.
1-1/3=2/3

Work done in 1 day.
1/15+1/10=1/6
Work in 2 days 2*1/6=1/3
Work remained 1-1/3=2/3

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