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9 men and 12 women can complete the job in 12 days.In how many days can 3 men and 4 women finish the same job working together ?
- a)36days
- b)42days
- c)30days
- d)28days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
9 men and 12 women can complete the job in 12 days.In how many days ca...
9m+12w = 1/12
3m+4w = ?
3(3m+4w) = 1/12
3m+4w = 1/36
3m+4w = ?
3(3m+4w) = 1/12
3m+4w = 1/36
Most Upvoted Answer
9 men and 12 women can complete the job in 12 days.In how many days ca...
Given information:
- 9 men and 12 women can complete the job in 12 days.
We need to find:
- In how many days can 3 men and 4 women finish the same job working together?
Let's assume that the work done by one man in one day is "m" units, and the work done by one woman in one day is "w" units.
Calculation:
- We are given that 9 men and 12 women can complete the job in 12 days.
- So, the total work done by them in one day is (9m + 12w).
- We can write the equation as: (9m + 12w) * 12 = 1 (as they complete the job in 12 days).
Now, we need to find the number of days required for 3 men and 4 women to finish the same job working together.
- Let's assume this number of days as "d".
- So, the total work done by 3 men and 4 women in one day is (3m + 4w).
- We can write the equation as: (3m + 4w) * d = 1.
To find the value of "d", we can equate the two equations:
(9m + 12w) * 12 = (3m + 4w) * d
Simplifying the equation:
108m + 144w = 3md + 4wd
108m + 144w = (3m + 4w) * d
We know that the left-hand side of the equation represents the work done by 9 men and 12 women in 12 days, which is equal to 1.
So, we can write this as: 108m + 144w = 1.
Substituting this value in the equation:
1 = (3m + 4w) * d
Simplifying further:
1 = 3md + 4wd
Comparing the coefficients of "m" and "w" on both sides of the equation:
3d = 108 => d = 36
Hence, 3 men and 4 women can finish the same job working together in 36 days. Therefore, the correct answer is option A, 36 days.
- 9 men and 12 women can complete the job in 12 days.
We need to find:
- In how many days can 3 men and 4 women finish the same job working together?
Let's assume that the work done by one man in one day is "m" units, and the work done by one woman in one day is "w" units.
Calculation:
- We are given that 9 men and 12 women can complete the job in 12 days.
- So, the total work done by them in one day is (9m + 12w).
- We can write the equation as: (9m + 12w) * 12 = 1 (as they complete the job in 12 days).
Now, we need to find the number of days required for 3 men and 4 women to finish the same job working together.
- Let's assume this number of days as "d".
- So, the total work done by 3 men and 4 women in one day is (3m + 4w).
- We can write the equation as: (3m + 4w) * d = 1.
To find the value of "d", we can equate the two equations:
(9m + 12w) * 12 = (3m + 4w) * d
Simplifying the equation:
108m + 144w = 3md + 4wd
108m + 144w = (3m + 4w) * d
We know that the left-hand side of the equation represents the work done by 9 men and 12 women in 12 days, which is equal to 1.
So, we can write this as: 108m + 144w = 1.
Substituting this value in the equation:
1 = (3m + 4w) * d
Simplifying further:
1 = 3md + 4wd
Comparing the coefficients of "m" and "w" on both sides of the equation:
3d = 108 => d = 36
Hence, 3 men and 4 women can finish the same job working together in 36 days. Therefore, the correct answer is option A, 36 days.
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