12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days.(A) 15 (B) 18 (C) 22 (D) data inadequate
Question
12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days.(A) 15 (B) 18 (C) 22 (D) data inadequate
Solution
The problem can be solved by first understanding the work rate of the men and women.
Step 1: Determine the work rate of the men and women.
- 12 men can complete the work in 4 days, so the work rate of one man is 1/(12*4) = 1/48 of the work per day.
- 15 women can complete the work in 4 days, so the work rate of one woman is 1/(15*4) = 1/60 of the work per day.
Step 2: Determine how much work has been completed and how much is left.
- 6 men worked for 2 days, so they completed 62(1/48) = 1/4 of the work.
- This means that 3/4 of the work is left to be completed.
Step 3: Determine how many women are needed to complete the remaining work in 3 days.
- If x women can complete the remaining work in 3 days, then x*(1/60)*3 = 3/4.
- Solving for x gives x = (3/4)/(3/60) = 15.
So, 15 women should be put on the job to complete the remaining work in 3 days. The answer is (A) 15.
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