4 men and 6 women can complete a job in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women take to complete the same job?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 40 days
Both groups finish the same job, so the total work they do (daily work × days) is equal. Setting the two equal gives the work of one man in terms of the work of one woman.
Let one man do \(m\) units and one woman \(w\) units of work in a day:
The first group does \(4m+6w\) a day, so in 8 days the job \(=32m+48w\) (1)
The second group does \(3m+7w\) a day, so in 10 days the job \(=30m+70w\) (2)
Setting (1) equal to (2): \(32m+48w=30m+70w\), so \(2m=22w\) and \(m=11w\): one man does the work of 11 women
Putting \(m=11w\) in (1), the job \(=32\times11w+48w=400w\), that is, 400 days of work for one woman
10 women share it, so they need \(400\div10=40\) days