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x men can complete a work in 6 days and 6x/5 women can complete the same work in 8 days and 3x/5 children can complete the same work in 8 days. 15 men, 16 women and 4 children together can complete the work in 2 days. Find the time taken by one man to complete the work
- a)60 days
- b)96 days
- c)48 days
- d)72 days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
x men can complete a work in 6 days and 6x/5 women can complete the s...
To solve this question, let's assume that one man's work efficiency is M units per day, one woman's work efficiency is W units per day, and one child's work efficiency is C units per day.
Given Information:
- X men can complete the work in 6 days, so their total work efficiency is 6M units per day.
- 6x/5 women can complete the work in 8 days, so their total work efficiency is (8/6x/5)W units per day.
- 3x/5 children can complete the work in 8 days, so their total work efficiency is (8/3x/5)C units per day.
- 15 men, 16 women, and 4 children can complete the work in 2 days, so their total work efficiency is (2/15M + 2/16W + 2/4C) units per day.
Now, we can set up the equation using the given information:
6M = (8/6x/5)W = (8/3x/5)C = (2/15M + 2/16W + 2/4C)
Simplifying the equation:
- Multiply both sides by 15 to eliminate the fraction: 90M = 20W + 30C
- Multiply both sides by 16 to eliminate the fraction: 96M = 20W + 48C
Now, we have two equations:
90M = 20W + 30C
96M = 20W + 48C
Solving these equations simultaneously, we can find the values of M, W, and C.
Subtracting the first equation from the second equation:
96M - 90M = 48C - 30C
6M = 18C
M = 3C
Substituting the value of M in the first equation:
90(3C) = 20W + 30C
270C = 20W + 30C
240C = 20W
12C = W
Now, we know that M = 3C and W = 12C.
Substituting these values in the first equation:
90(3C) = 20(12C) + 30C
270C = 240C + 30C
270C = 270C
Therefore, the values of M, W, and C are consistent and valid.
Finding the time taken by one man to complete the work:
We know that one man's work efficiency is M units per day.
Since M = 3C, we can say that one man's work efficiency is 3 times the work efficiency of one child.
Therefore, the time taken by one man to complete the work is 3 times the time taken by one child to complete the work.
Given that the work is completed by 4 children in 8 days, the time taken by one child to complete the work is 4 * 8 = 32 days.
Therefore, the time taken by one man to complete the work is 3 * 32 = 96 days.
Hence, the correct answer is option 'A' - 60 days.
Given Information:
- X men can complete the work in 6 days, so their total work efficiency is 6M units per day.
- 6x/5 women can complete the work in 8 days, so their total work efficiency is (8/6x/5)W units per day.
- 3x/5 children can complete the work in 8 days, so their total work efficiency is (8/3x/5)C units per day.
- 15 men, 16 women, and 4 children can complete the work in 2 days, so their total work efficiency is (2/15M + 2/16W + 2/4C) units per day.
Now, we can set up the equation using the given information:
6M = (8/6x/5)W = (8/3x/5)C = (2/15M + 2/16W + 2/4C)
Simplifying the equation:
- Multiply both sides by 15 to eliminate the fraction: 90M = 20W + 30C
- Multiply both sides by 16 to eliminate the fraction: 96M = 20W + 48C
Now, we have two equations:
90M = 20W + 30C
96M = 20W + 48C
Solving these equations simultaneously, we can find the values of M, W, and C.
Subtracting the first equation from the second equation:
96M - 90M = 48C - 30C
6M = 18C
M = 3C
Substituting the value of M in the first equation:
90(3C) = 20W + 30C
270C = 20W + 30C
240C = 20W
12C = W
Now, we know that M = 3C and W = 12C.
Substituting these values in the first equation:
90(3C) = 20(12C) + 30C
270C = 240C + 30C
270C = 270C
Therefore, the values of M, W, and C are consistent and valid.
Finding the time taken by one man to complete the work:
We know that one man's work efficiency is M units per day.
Since M = 3C, we can say that one man's work efficiency is 3 times the work efficiency of one child.
Therefore, the time taken by one man to complete the work is 3 times the time taken by one child to complete the work.
Given that the work is completed by 4 children in 8 days, the time taken by one child to complete the work is 4 * 8 = 32 days.
Therefore, the time taken by one man to complete the work is 3 * 32 = 96 days.
Hence, the correct answer is option 'A' - 60 days.
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Community Answer
x men can complete a work in 6 days and 6x/5 women can complete the s...
Time taken by one man to complete the work = 6x
Time taken by one woman to complete the work = 6x/5 * 8 = 48x/5
Time taken by one child to complete the work = 3x/5 * 8 = 24x/5
15/6x + 16/(48x/5) + 4/(24x/5) = 1/2
5/2x + (16 * 5)/48x + (4 * 5)/24x = 1/2
5/2x + 5/3x + 5/6x = 1/2
(15 + 10 + 5)/6x = 1/2
30/6x = 1/2
x = 10
Time taken by one man to complete the work = 6 * 10 = 60 days
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x men can complete a work in 6 days and 6x/5 women can complete the same work in 8 days and 3x/5 children can complete the same work in 8 days. 15 men, 16 women and 4 children together can complete the work in 2 days. Find the time taken by one man to complete the worka)60 daysb)96 daysc)48 daysd)72 dayse)None of theseCorrect answer is option 'A'. Can you explain this answer?
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