2 men can complete a piece of work in 18 days while 6 women can do it in 6 days. In how many days can 3 women and 6 men complete it?
4 days
To solve this problem, we need to determine the combined work rate of 3 women and 6 men and calculate how long it would take them to complete the work. Let's analyze the given information:
Step 1: Calculate the work rate of men. 2 men can complete the work in 18 days. Therefore, 1 man's work rate is \( \frac{1}{2 \times 18} = \frac{1}{36} \) of the work per day.
Step 2: Calculate the work rate of women. 6 women can complete the work in 6 days. Therefore, 1 woman's work rate is \( \frac{1}{6 \times 6} = \frac{1}{36} \) of the work per day.
Step 3: Calculate the combined work rate for 3 women and 6 men. The work rate for 3 women is \( 3 \times \frac{1}{36} = \frac{3}{36} = \frac{1}{12} \) of the work per day. The work rate for 6 men is \( 6 \times \frac{1}{36} = \frac{6}{36} = \frac{1}{6} \) of the work per day.
Adding these, the combined work rate for 3 women and 6 men is:
\(\frac{1}{12} + \frac{1}{6} = \frac{1 \times 1 + 2 \times 1}{12} = \frac{3}{12} = \frac{1}{4}\)
Step 4: Calculate the time taken for the combined group to complete the work. Since the combined work rate is \(\frac{1}{4}\) of the work per day, it will take:
\( \frac{1}{\frac{1}{4}} = 4 \) days
Therefore, 3 women and 6 men can complete the work in 4 days.
Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
