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8 men can complete a piece of work in 18 days, 18 women complete in 10 days while 6 children complete in 12 days. 4 children, 12 men and 20 women work for 2 days. If only children were to complete the remaining work in 1 day. How many children are required.
- a)36
- b)24
- c)18
- d)Can’t determine
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
8 men can complete a piece of work in 18 days, 18 women complete in 10...
8 M = 18 days
M = 18 × 8 = 144 days
W = 18 × 10 = 180 days
C = 6 × 12 = 72 days
Let work be 720 unit then
M = 5 unit daily
W = 4 unit daily
C = 10 unit daily
4 children, 12 men, 20 women = 40 + 60 + 80 = 180 unit × 2 = 360 unit
Rest 720 – 360 = 360 unit
So, no. of children who complete in 1 day = 360/10 = 36
Most Upvoted Answer
8 men can complete a piece of work in 18 days, 18 women complete in 10...
Work Calculation by Men, Women, and Children
To find out how many children are required to complete the remaining work, we first need to determine the work done by each group (men, women, and children) and their combined effort.
Work Rates
- Men's Work Rate:
8 men can complete the work in 18 days,
Therefore, the work done by 1 man in 1 day = 1 / (8 * 18) = 1/144.
- Women's Work Rate:
18 women can complete the work in 10 days,
Therefore, the work done by 1 woman in 1 day = 1 / (18 * 10) = 1/180.
- Children's Work Rate:
6 children can complete the work in 12 days,
Therefore, the work done by 1 child in 1 day = 1 / (6 * 12) = 1/72.
Combined Work Rate of 4 Children, 12 Men, and 20 Women
- Work done by 4 Children in 1 day = 4 * (1/72) = 1/18.
- Work done by 12 Men in 1 day = 12 * (1/144) = 1/12.
- Work done by 20 Women in 1 day = 20 * (1/180) = 1/9.
Total Work Done in 1 Day
- Total work done in 1 day = (1/18 + 1/12 + 1/9).
Finding a common denominator (36):
- Work done = (2/36 + 3/36 + 4/36) = 9/36 = 1/4.
In 2 days, they can complete:
- Work done in 2 days = 2 * (1/4) = 1/2.
Remaining Work
The remaining work after 2 days is:
- Total work - Work done = 1 - 1/2 = 1/2.
Work Done by Children in 1 Day
To find how many children are needed to complete the remaining 1/2 work in 1 day:
- Each child can do 1/72 of work in 1 day. Let 'x' be the number of children required:
- x * (1/72) = 1/2.
Solving for x:
- x = (1/2) * 72 = 36.
Thus, 36 children are required to complete the remaining work in 1 day.
Correct Answer: a) 36.
To find out how many children are required to complete the remaining work, we first need to determine the work done by each group (men, women, and children) and their combined effort.
Work Rates
- Men's Work Rate:
8 men can complete the work in 18 days,
Therefore, the work done by 1 man in 1 day = 1 / (8 * 18) = 1/144.
- Women's Work Rate:
18 women can complete the work in 10 days,
Therefore, the work done by 1 woman in 1 day = 1 / (18 * 10) = 1/180.
- Children's Work Rate:
6 children can complete the work in 12 days,
Therefore, the work done by 1 child in 1 day = 1 / (6 * 12) = 1/72.
Combined Work Rate of 4 Children, 12 Men, and 20 Women
- Work done by 4 Children in 1 day = 4 * (1/72) = 1/18.
- Work done by 12 Men in 1 day = 12 * (1/144) = 1/12.
- Work done by 20 Women in 1 day = 20 * (1/180) = 1/9.
Total Work Done in 1 Day
- Total work done in 1 day = (1/18 + 1/12 + 1/9).
Finding a common denominator (36):
- Work done = (2/36 + 3/36 + 4/36) = 9/36 = 1/4.
In 2 days, they can complete:
- Work done in 2 days = 2 * (1/4) = 1/2.
Remaining Work
The remaining work after 2 days is:
- Total work - Work done = 1 - 1/2 = 1/2.
Work Done by Children in 1 Day
To find how many children are needed to complete the remaining 1/2 work in 1 day:
- Each child can do 1/72 of work in 1 day. Let 'x' be the number of children required:
- x * (1/72) = 1/2.
Solving for x:
- x = (1/2) * 72 = 36.
Thus, 36 children are required to complete the remaining work in 1 day.
Correct Answer: a) 36.
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