12 men can complete work in 6 days whereas 10 men and 21 women take 3 days to…
2024
12 men can complete work in 6 days whereas 10 men and 21 women take 3 days to finish the same work in how many days can 12 women alone complete.
- A.
6
- B.
7
- C.
8
- D.
9
Attempted by 32 students.
Show answer & explanation
Correct answer: D
Key idea: Use work = rate × time to find individual rates and then the combined rate of women.
Step 1: Find one man’s daily work. Twelve men finish in 6 days, so total work = 1. One man’s one-day work = 1/(12×6) = 1/72.
Step 2: Let a woman’s one-day work be w. Ten men and 21 women finish in 3 days, so their combined one-day work = 1/3. Thus 10×(1/72) + 21w = 1/3.
Step 3: Solve for w. 10×(1/72) = 10/72 = 5/36. So 21w = 1/3 − 5/36 = 12/36 − 5/36 = 7/36. Therefore w = (7/36)/21 = 1/108.
Step 4: Find time for 12 women. Combined daily work of 12 women = 12×(1/108) = 1/9, so they complete the work in 9 days.
Answer: 12 women alone can complete the work in 9 days.