Question

Q 55 Paul and Peter undertake to do a piece
of work for $500. Paul alone can do a
work in 5 days, Lisa alone can do it in 10
days. If Peter helps them they can finish
the work in 3 days. What will be the
approximate share of Peter?

Answer 1

Given :

Paul and Peter undertake to do a piece  of work for $500

Paul alone can do a  work in 5 days  

Lisa alone can do it in 10  days.

With the help of Peter they can finish  the work in 3 days

To Find :

The  approximate share amount of Peter

Solution :

Paul alone can do a  work in 5 days  

So, Paul 1 day work = $\dfrac{1}{5}$

With the help of Peter they can finish  the work in 3 days

∴ Paul 3 days work = $\dfrac{3}{5}$

Lisa alone can do it in 10  days

So, Lisa 1 day work = $\dfrac{1}{10}$

∵  With the help of Peter they can finish  the work in 3 days

∴ Lisa 3 days work = $\dfrac{3}{10}$

Let Peter alone can complete work in x days

So, Peter 3 days work = 1 - ( Paul 3 days work + Lisa 3 days work )

                                      = 1 - ( $\dfrac{3}{5}$ + $\dfrac{3}{10}$ )

                                      = 1 - (  $\dfrac{6+3}{10}$ )

                                      = 1 -  $\dfrac{9}{10}$

                                      =  $\dfrac{10-9}{10}$  

                                      =  $\dfrac{1}{10}$

Again

The ratio of their share = $\dfrac{3}{5}$ :  $\dfrac{3}{10}$  : $\dfrac{1}{10}$

i.e                                    = 6 : 3 : 1

Now, Peter's share =  $\dfrac{1}{6+3+1}$ × $ 500

                               = $\dfrac{1}{10}$ × $ 500

∴ Peter's share = $ 50

Hence, The share amount of Peter is $50  . Answer