Number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days
Given that Â
A team of seven workers started a job, which can be done in 11 days.
On the morning of the fourth day, several people left the team. The rest of team finished the job in 14 days. Â
Need to determine how many people left the team. Â
Let say complete work be represented by variable W.
=> work done by 7 workers in 11 days = W
[tex]\Rightarrow \text {work done by } 1 \text { worker in } 11 \text { days }=\frac{\mathrm{W}}{7}[/tex]
[tex]\Rightarrow \text {work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{7} \div 11=\frac{W}{77}[/tex]
As its given that for three days all the seven workers worked.
Work done by 7 worker in 3 day is given as:
[tex]=7 \times 3 \times \text { work done by } 1 \text { worker in } 1 \text { day }[/tex]
[tex]=7 \times 3 \times \frac{W}{77}=\frac{3W}{11}[/tex]
Work remaining after 3 days = Complete Work - Work done by 7 worker in 3 day
[tex]=W-\frac{3 W}{11}=\frac{8 W}{11}[/tex]
It is also given that on fourth day some workers are left.
Let workers left on fourth day = x
So Remaining workers = 7 – x
And these 7 – x workers completed remaining work in 14 days
[tex]\begin{array}{l}{\text { As work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{77}} \\\\ {\text { So work done by } 1 \text { worker in } 14 \text { days }=\frac{W}{77} \times 14=\frac{2 \mathrm{W}}{11}} \\\\ {\text { So work done by } 7-x \text { worker in } 14 \text { days }=\frac{2 \mathrm{W}}{11}(7-x)}\end{array}[/tex]
As Work remaining after 3 days = [tex]\frac{8W}{11}[/tex] and this is the same work done by 7- x worker in 14 days
[tex]\begin{array}{l}{\Rightarrow \frac{\mathrm{8W}}{11}=\frac{2 \mathrm{W}}{11}(7-x)} \\\\ {=>4=7-x} \\\\ {=>x=7-4=3}\end{array}[/tex]
Workers left on fourth day = x = 3
Hence number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days.
