A canal 12 km long is to be dug in 90 days, and 150 labourers are put on the job. After 60 days only 6 km of the canal has been dug. How many more labourers, working at the same rate, must be added so that the canal is finished on time?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 150
The work done is proportional to labourers \(\times\) days. The first 60 days tell us how many labourer-days one kilometre needs.
Work so far: \(150\times60=9000\) labourer-days for 6 km
One km needs \(\displaystyle \frac{9000}{6}=1500\) labourer-days
Left: \(12-6=6\) km, needing \(6\times1500=9000\) labourer-days
Days left \(=90-60=30\); labourers needed \(\displaystyle =\frac{9000}{30}=300\)
Extra labourers \(=300-150=150\)
150 more labourers must be added.
Why the other options are incorrect
Option (1) 100 — Incorrect. 250 labourers in 30 days give 7500 labourer-days, only 5 km.
Option (3) 200 — Incorrect. 350 labourers would finish the 6 km in about 26 days, more than needed.
Option (4) 300 — Incorrect. 300 is the total number needed; 150 are already at work.