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4 women and 12 children together take 4 days to complete a piece of work. How many days will 8 children alone take to complete the piece of work if 4 women can complete the piece of work in 8 days?
- a)24
- b)12
- c)16
- d)18
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
4 women and 12 children together take 4 days to complete a piece of w...
Given,
4 women can complete the work in 8 days
1 day work of a woman = 1/32
(4 women + 12 children)'s 1 day work =1/4
12 children's 1 day work
= 1/4 − 4/32
= 1/4 − 1/8 = (2 − 1)/8 = 1/8
12 children can complete the work in 8 days
So, 8 children will complete the work = 12 × 88 = 12 days.
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Community Answer
4 women and 12 children together take 4 days to complete a piece of w...
Understanding the Work Done by Women and Children
To solve the problem, we first need to determine the work rates of the women and children involved.
1. Work Done by Women
- Given: 4 women can complete the work in 8 days.
- Therefore, the total work done by 4 women in 8 days = 1 work unit.
- The work rate of 4 women = \( \frac{1 \text{ work unit}}{8 \text{ days}} = \frac{1}{8} \text{ work units per day} \).
- Hence, the work rate of 1 woman = \( \frac{1}{8} \div 4 = \frac{1}{32} \text{ work units per day} \).
2. Work Done by Children
- 4 women and 12 children together complete the work in 4 days.
- Their combined work rate = \( \frac{1 \text{ work unit}}{4 \text{ days}} = \frac{1}{4} \text{ work units per day} \).
- Work rate of 4 women = \( \frac{1}{8} \text{ work units per day} \).
- Therefore, work rate of 12 children = \( \frac{1}{4} - \frac{1}{8} = \frac{2}{8} - \frac{1}{8} = \frac{1}{8} \text{ work units per day} \).
- Thus, the work rate of 1 child = \( \frac{1}{8} \div 12 = \frac{1}{96} \text{ work units per day} \).
3. Work Rate of 8 Children
- Work rate of 8 children = \( 8 \times \frac{1}{96} = \frac{8}{96} = \frac{1}{12} \text{ work units per day} \).
4. Days Taken by 8 Children to Complete the Work
- To find the number of days taken by 8 children to complete the work:
- Total days = \( \frac{1 \text{ work unit}}{\frac{1}{12} \text{ work units per day}} = 12 \text{ days} \).
Thus, the correct answer is option 'B'.
To solve the problem, we first need to determine the work rates of the women and children involved.
1. Work Done by Women
- Given: 4 women can complete the work in 8 days.
- Therefore, the total work done by 4 women in 8 days = 1 work unit.
- The work rate of 4 women = \( \frac{1 \text{ work unit}}{8 \text{ days}} = \frac{1}{8} \text{ work units per day} \).
- Hence, the work rate of 1 woman = \( \frac{1}{8} \div 4 = \frac{1}{32} \text{ work units per day} \).
2. Work Done by Children
- 4 women and 12 children together complete the work in 4 days.
- Their combined work rate = \( \frac{1 \text{ work unit}}{4 \text{ days}} = \frac{1}{4} \text{ work units per day} \).
- Work rate of 4 women = \( \frac{1}{8} \text{ work units per day} \).
- Therefore, work rate of 12 children = \( \frac{1}{4} - \frac{1}{8} = \frac{2}{8} - \frac{1}{8} = \frac{1}{8} \text{ work units per day} \).
- Thus, the work rate of 1 child = \( \frac{1}{8} \div 12 = \frac{1}{96} \text{ work units per day} \).
3. Work Rate of 8 Children
- Work rate of 8 children = \( 8 \times \frac{1}{96} = \frac{8}{96} = \frac{1}{12} \text{ work units per day} \).
4. Days Taken by 8 Children to Complete the Work
- To find the number of days taken by 8 children to complete the work:
- Total days = \( \frac{1 \text{ work unit}}{\frac{1}{12} \text{ work units per day}} = 12 \text{ days} \).
Thus, the correct answer is option 'B'.
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4 women and 12 children together take 4 days to complete a piece of work. How many days will 8 children alone take to complete the piece of work if 4 women can complete the piece of work in 8 days?a)24b)12c)16d)18e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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