# 6th Class Mathematics Time and Work TIME AND WORK

TIME AND WORK

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.

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.

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