A contractor undertakes to build a wall in 45 days and starts with a certain number of workers. After 15 days he finds that, at this rate, only 75% of the work will be completed in the 45 days. So he adds 45 more workers, and the work is completed on time. How many workers did he start with?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 90
At the starting rate the first workers would finish 75% in 45 days, so in the first 15 days (one-third of the time) they did 25% of the work. The work left must be done in the remaining 30 days, and the number of workers needed is in proportion to the work per day.
Let the contractor start with \(N\) workers; in 15 days they do \(\frac{1}{3}\times75\%=25\%\) of the work
Work left \(=75\%\), to be done in \(45-15=30\) days
In 30 days, \(N\) workers would do \(2\times25\%=50\%\); doing 75% needs \(\displaystyle \frac{75}{50}N=1.5N\) workers
Workers added \(=1.5N-N=0.5N=45\), so \(N=90\)