# 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?

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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.

“Complete step-by-step answer:”

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.

“Complete step-by-step answer:”

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.

Last updated date: 18th Sep 2023

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