A contractor undertakes to lay a road in 50 days and starts with a certain number of workers. After 10 days he finds that, at this rate, only 75% of the work will be completed in the 50 days. So he adds 25 more workers, and the work is completed on time. How many workers did he start with?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 60
At the starting rate the first workers would finish 75% in 50 days, so in the first 10 days (one-fifth of the time) they did 15% of the work. The work left must be done in the remaining 40 days, and the number of workers needed is in proportion to the work per day.
Let the contractor start with \(N\) workers; in 10 days they do \(\frac{1}{5}\times75\%=15\%\) of the work
Work left \(=85\%\), to be done in \(50-10=40\) days
In 40 days, \(N\) workers would do \(4\times15\%=60\%\); doing 85% needs \(\displaystyle \frac{85}{60}N=\frac{17}{12}N\) workers
Workers added \(\displaystyle =\frac{17}{12}N-N=\frac{5}{12}N=25\), so \(N=60\)