**Category : **6th Class

**Learning Objective**

To learn about time taken to complete a work.

To find number of person required to complete a given piece of work.

** **

**TIME AND WORK**

If a does a work in ‘a’ days then in 1 day A does \[\frac{1}{a}\] of the work.

If B does a work in 'b' days then in 1 day B does \[\frac{1}{b}\] of the work.

Then in 1 day, if A and B work together, their combined work is \[\frac{1}{a}+\frac{1}{b}\,\text{or}\,\frac{a+b}{ab}\]

The work will be completed when 1 unit of work is completed.

Now using Unitary Method

Time required to complete \[\frac{a+b}{ab}\] work = 1 day

\[\therefore \] Time required to complete 1 work \[=\frac{1}{\frac{a+b}{ab}}\,=\frac{ab}{a+b}\]

Here we should recollect our knowledge of variation.

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**For example:**

A and B can do a piece of work in 20 days and 30 days respectively They work together and A leaves 5 days before the work is finished. B finishes the remaining work alone. In how many days is the total work finished?

**Solution.** Let the work is completed in 'f days. A works for (t - 5) days and B works for 't' days.

Now A's work + B's work = 1

\[\therefore \]\[\frac{t-5}{20}+\frac{t}{30}\,=1\,\,\Rightarrow \,\,3t-15+2t\,=60\,\Rightarrow \,5t=60+15\]

\[\Rightarrow \,\,5t+75\,\,\Rightarrow \,\,t=15\] days.

\[\therefore \] Time required to finish the work is 15 days.

*play_arrow*TIME AND WORK

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