Question

anorge
doc
3
Paul and Lisa can do a piece of work in 40 and 60 days respectively. They began the work together, but Paul left after some days and Lisa finished the
remaining work in 40 days. After how many days did Paul leave?​

Answer 1

Given:  

Paul and Lisa can do a piece of work in 40 days and 60 days.  

Lisa completed the remaining work in 40 days  

To find:  

The number of days after which Paul left

Solution:  

In 1 day, the work done by Paul =   $\frac{1}{40}$

and  

In 1 day, the work done by Lisa =  $\frac{1}{60}$

So, in 1 day, the work done by Paul and Lisa together will be = [$\frac{1}{40} + \frac{1}{60}$]

Let "x" days be the no. of days after which Paul left the work .

It is given to us that after working together for "x" days, Paul leaves and Lisa completes the remaining work in 40 days.

So, we can form the equation for the whole work to be done as,  

$x[\frac{1}{40} + \frac{1}{60}] + \frac{40}{60} = 1$

⇒ $x[\frac{3+2}{120} ] + \frac{2}{3} = 1$  

⇒   $x[\frac{5}{120} ] + \frac{2}{3} = 1$

⇒   $x[\frac{1}{24} ] = 1 - \frac{2}{3}$

⇒   $x[\frac{1}{24} ] = \frac{3- 2}{3}$

⇒   $x = \frac{1\times24}{3}$

⇒   $x = \bold{8 \:days}$

Thus, Paul left the work after 8 days.  

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