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Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?
- a)8
- b)12
- c)7
- d)49
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three men, four women and six children can complete a work in seven da...
Let 1 woman’s 1 day’s work = x
⇒ 1 man’s 1 day’s work = x/2 and 1 child’s 1 day’s work = x/4
⇒ (3x/2 + 4x + 6x/4) = 1/7
⇒ 28x/4 = 1/7
⇒ x = (1/7 × 4/28) = 1/49
⇒ 1 woman can complete the work in 49 days.
∴ To complete the work in 7 days, number of women required = (49/7) = 7
Most Upvoted Answer
Three men, four women and six children can complete a work in seven da...
Given:
- Three men, four women, and six children can complete a work in seven days.
- A woman does double the work a man does.
- A child does half the work a man does.
To find:
- How many women alone can complete this work in seven days.
Assumptions:
- The work done by each person is directly proportional to the number of days.
- All men, women, and children have the same level of efficiency.
Solution:
Step 1: Calculate the work done by each person per day
Let's assume the work done by a man per day is M.
- A woman does double the work a man does, so the work done by a woman per day is 2M.
- A child does half the work a man does, so the work done by a child per day is 0.5M.
Step 2: Calculate the total work done in seven days
Since three men, four women, and six children can complete the work in seven days:
Total work done in seven days = (3M + 4(2M) + 6(0.5M)) * 7
Simplifying this equation:
Total work done in seven days = (3M + 8M + 3M) * 7
= 14M * 7
= 98M
Step 3: Calculate the work done by a woman per day
Since a woman does double the work a man does:
2M = (1/7) * 98M
2M = 14M
M = 1/7
So, the work done by a woman per day = 2M = 2 * (1/7) = 2/7
Step 4: Calculate the number of women required to complete the work in seven days
To calculate the number of women required to complete the work in seven days, we divide the total work done in seven days by the work done by a woman per day:
Number of women required = (Total work done in seven days) / (Work done by a woman per day)
= 98M / (2/7)
= 98M * (7/2)
= 49 * 7
= 343
Therefore, seven women alone can complete this work in seven days (Option C).
- Three men, four women, and six children can complete a work in seven days.
- A woman does double the work a man does.
- A child does half the work a man does.
To find:
- How many women alone can complete this work in seven days.
Assumptions:
- The work done by each person is directly proportional to the number of days.
- All men, women, and children have the same level of efficiency.
Solution:
Step 1: Calculate the work done by each person per day
Let's assume the work done by a man per day is M.
- A woman does double the work a man does, so the work done by a woman per day is 2M.
- A child does half the work a man does, so the work done by a child per day is 0.5M.
Step 2: Calculate the total work done in seven days
Since three men, four women, and six children can complete the work in seven days:
Total work done in seven days = (3M + 4(2M) + 6(0.5M)) * 7
Simplifying this equation:
Total work done in seven days = (3M + 8M + 3M) * 7
= 14M * 7
= 98M
Step 3: Calculate the work done by a woman per day
Since a woman does double the work a man does:
2M = (1/7) * 98M
2M = 14M
M = 1/7
So, the work done by a woman per day = 2M = 2 * (1/7) = 2/7
Step 4: Calculate the number of women required to complete the work in seven days
To calculate the number of women required to complete the work in seven days, we divide the total work done in seven days by the work done by a woman per day:
Number of women required = (Total work done in seven days) / (Work done by a woman per day)
= 98M / (2/7)
= 98M * (7/2)
= 49 * 7
= 343
Therefore, seven women alone can complete this work in seven days (Option C).
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Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?a)8b)12c)7d)49Correct answer is option 'C'. Can you explain this answer?
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