Five men and nine women can do a piece of work in 10 days days. Six men and…
20252024202520232025
Five men and nine women can do a piece of work in 10 days days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work ?
- A.
24
- B.
18
- C.
20
- D.
22
Attempted by 8 students.
Show answer & explanation
Correct answer: C
Answer: 20 days
Key idea: equate the total work expressed by each group to find the relation between one man's rate and one woman's rate, then compute the time for three men and three women.
Let m = one man's work per day and w = one woman's work per day.
From the first situation: (5m + 9w) × 10 = total work.
From the second situation: (6m + 12w) × 8 = total work. Equate the two expressions:
50m + 90w = 48m + 96w ⇒ 2m = 6w ⇒ m = 3w.
Compute total work in terms of w: 5m + 9w = 15w + 9w = 24w, so total work = 24w × 10 = 240w.
Rate of 3 men and 3 women: 3m + 3w = 9w + 3w = 12w.
Time required = total work ÷ daily rate = 240w ÷ 12w = 20 days.