Question

The mean monthly salary paid to 75 workers in a factory is Rs 5680. The mean salary of 25 of them is Rs 5400 and that of 30 others is Rs 5700. Find the mean salary of the remaining workers.

Answer 1

Mean monthly salary paid to 75 workers = Rs 5680
Mean salary of 25 workers = Rs 5400
Sum of the monthly salaries paid to 25 workers = Rs (5400$\times$25) = Rs 135000
Mean salary of the other 30 workers = Rs 5700
Sum of the monthly salaries of the other 30 workers = Rs (5700$\times$30) = Rs 171000
Let the sum of the salaries of the remaining 30 workers be Rs x.
$$\begin{gathered} \mathrm{Mean}\mathrm{monthly}\mathrm{salary}\mathrm{paid}\mathrm{to}75\mathrm{workers}=\frac{135000+171000+x}{75} \\ \Rightarrow 5680=\frac{306000+x}{75} \\ \Rightarrow 426000=306000+x \\ \Rightarrow x=120000 \\ \mathrm{Therefore},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{salaries}\mathrm{of}\mathrm{the}\mathrm{remaining}20\mathrm{workers}\mathrm{is}\mathrm{Rs}120000. \\ \mathrm{Mean}\mathrm{salary}\mathrm{of}\mathrm{the}\mathrm{remaining}20\mathrm{workers}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{salaries}\mathrm{of}20\mathrm{workers}}{20} \\ =\frac{120000}{20}=\mathrm{Rs}6000 \\ \mathrm{Hence},\mathrm{the}\mathrm{mean}\mathrm{salary}\mathrm{of}\mathrm{the}\mathrm{remaining}20\mathrm{workers}\mathrm{is}\mathrm{Rs}6000. \end{gathered}$$