A 12-hectare field is reaped by 1 man, 2 women and 3 children together in 24 days. The working capacities of a man, a woman and a child are in the ratio 7 : 4 : 2. In how many days will 2 men, 1 woman and 5 children reap a 14-hectare field?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21
Read the ratio as units of work per day: a man 7, a woman 4, a child 2. The work needed is proportional to the area reaped.
First group per day: \(1\times7+2\times4+3\times2=21\) units
Work for 12 hectares \(=21\times24=504\) units, that is \(\frac{504}{12}=42\) units per hectare
Work for 14 hectares \(=42\times14=588\) units
Second group per day: \(2\times7+1\times4+5\times2=28\) units
Time \(\displaystyle =\frac{588}{28}=21\) days