6 women and 4 men can complete a work in 10 days, while 4 women and 5 men complete it in 10 days. In how many days will 8 women complete it?

Correct — C.
Both groups finish in the same 10 days, so their daily work is equal
6W + 4M = 4W + 5M
Subtract 4W + 4M from both sides: 2W = 1M

Replace each man by 2 women: 6W + 4M = 6W + 8W = 14 women
Check the other group: 4W + 5M = 4W + 10W = 14 women
Whole job = 14 × 10 = 140 woman-days

8 women: 140 ÷ 8 = 17.5 days → option (c)

Why the others are wrong

• (a)
  12 days — 12 days gives 8 × 12 = 96 woman-days, but the job is 140 woman-days. Eight women finish only about 69% of it in 12 days.
• (b)
  14 days — 14 days gives 8 × 14 = 112 woman-days, not 140. The number 14 belongs to the group — 6W + 4M is worth 14 women — not to the time.
• (d)
  15 days — 15 days gives 8 × 15 = 120 woman-days, 20 short of the 140 the job needs. Eight women need 20 ÷ 8 = 2.5 more days.

When two different teams finish the same job in the same time, their daily outputs are equal. Setting the teams equal and cancelling what they share gives the exchange rate between workers — here 1 man = 2 women.

Convert everyone into one kind of worker. The job is then a fixed number of worker-days, and days = worker-days ÷ workers.

Key facts

• Equal time on the same job means equal work per day
• Here 1 man does the work of 2 women
• Days = total worker-days ÷ number of workers

Common traps

• Treating men and women as equal workers: 10 people × 10 days ÷ 8 gives 12.5 days
• Reading 2W = 1M backwards as 1 woman = 2 men, which would make 8 women finish in 10 days

No directly related past PYQ was found.