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# A can do work in 15 days and B can do the same work in 20 days. If A and B have done work for 4 days together, the fraction of work left?  Verified
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Hint – The number of days on which the work can be completed by A and B separately is given to us. Now A and B have worked together for 4 days and we need to find the fraction of work which is left. SO let the total work to be done by A and B be P. Using the unitary methods calculate the work done by A and B by per day and using this calculate the work done by them together in 4 days.

It is given that A can do a work in 15 days and B can do a work in 20 days.
If A and B have done work for 4 days together then we have to find out the fraction of work left.
Let the total work be P.
So, the work done by A per day is the ratio of total work divided by the number of days in which A can do the work.
So, the work done by A per day $= \dfrac{P}{{15}}$.
Similarly, the work done by B per day $= \dfrac{P}{{20}}$.
Now the work done by A and B in four days is
$\Rightarrow \left( {\dfrac{P}{{15}} + \dfrac{P}{{20}}} \right) \times 4$
Now simplify this we have
$\Rightarrow \left( {\dfrac{P}{{15}} + \dfrac{P}{{20}}} \right) \times 4 = \dfrac{{28}}{{60}}P$
So, the work left is total work minus the work done by A and B in four days.
So, work left $= P - \dfrac{{28}}{{60}}P = \dfrac{{32}}{{60}}P = \dfrac{8}{{15}}P$
So, the fraction of work left is $\dfrac{8}{{15}}$.
So, this is the required answer.

Note – Whenever we face such types of problems the key concept here is to simply apply a unitary method to calculate the work done by the individuals per day then use the conditions and information given in the question to get the required entity.