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. How many people left the team? Show your work in an equation

Number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 daysSolution:Given that  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.  Need to determine how many people left the team.  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.