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The work of 4 men is equal to the work of 6 women and the work of 9 women is equal to the work of 12 boys. 8 men and 6 women working 8 hours a day complete work is 15 days. In how many days 2 men, 3 women and 4 boys together working 6 hours daily will complete that work?
- a)40
- b)45
- c)60
- d)48
- e)50
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The work of 4 men is equal to the work of 6 women and the work of 9 w...
Given
The work of 4 men is equal to the work of 6 women and the work of 9 women is equal to the work of 12 boys.
8 men and 6 women working 8 hours a day complete work is 15 days.
Assumption:
Efficiency of a man = M unit work/hour.
Efficiency of a woman = W unit work/hour & efficiency of a boy = B unit work/hour.
Calculation:
⇒ 4M = 6W
⇒ 2M = 3W
The work of 9 women is equal to work of 12 boys.
⇒ 9W = 12B
⇒ 3W = 4B
∴ 2M = 3W = 4B
In 1 day, working 8 hours per day, total work done by 1 man = 8M
In 1 day, working 8 hours per day, total work done by 1 woman = 6W
8 men and 6 women working 8 hours a day complete a work is 15 days.
∴ Total work = (8M × 8 × 15) + (6W × 8 × 15) = 240 × (4M + 3W)
Assume that, in n days, 2 men, 3 women and 4 boys together working 6 hours daily will completer that work.
Total work done in this case = (2 × M × 6 × n) + (3 × W × 6 × n) + (4 × B × 6 × n)
In both cases total work will be equal.
⇒ (12M + 18W + 24B) × n = 240 × (4M + 3W)
⇒ 6 × (2M + 3W + 4B) × n = 240 × (4M + 3W)
⇒ (2M + 3W + 4B) × n = 40 × (4M + 3W)
⇒ (3W + 3W + 3W) × n = 40 × (6W + 3W)
⇒ n = 40
In 40 days 2 men, 3 women and 4 boys together working 6 hours daily will complete that work.
Hence, the correct option is (A).
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Community Answer
The work of 4 men is equal to the work of 6 women and the work of 9 w...
Let's break down the problem step by step to find the solution.
Given information:
- The work of 4 men is equal to the work of 6 women.
- The work of 9 women is equal to the work of 12 boys.
- 8 men and 6 women working 8 hours a day complete work in 15 days.
1. Finding the work ratio:
- Let's assume that the work done by 1 man in 1 day is M and the work done by 1 woman in 1 day is W.
- From the given information, we can write the following equations:
4M = 6W (work of 4 men is equal to the work of 6 women)
9W = 12B (work of 9 women is equal to the work of 12 boys)
2. Finding the work done by men and women in 1 day:
- If 8 men and 6 women complete the work in 15 days, we can find the work done by men and women in 1 day.
- Work done by men in 1 day = (8 men * 8 hours) / 15 days = 64M/15
- Work done by women in 1 day = (6 women * 8 hours) / 15 days = 48W/15
3. Finding the work done by 2 men, 3 women, and 4 boys in 1 day:
- We need to find the work done by 2 men, 3 women, and 4 boys in 1 day to determine how many days they will complete the work.
- Work done by 2 men in 1 day = 2M
- Work done by 3 women in 1 day = 3W
- Work done by 4 boys in 1 day = 4B
4. Finding the number of days required:
- Now, we can set up a proportion to find the number of days required:
(Work done by 2 men)/(Work done by 3 women + Work done by 4 boys) = (Number of days required)/(15 days)
(2M)/(3W + 4B) = X/15
- Substituting the values from step 2 and step 3 into the proportion:
(2M)/(3W + 4B) = X/15
(2M)/(3W + 4B) = X/15
(2M)/(3W + 4B) = X/15
(2M)/(3W + 4B) = X/15
- Simplifying the equation:
(8M)/(48W + 64B) = X/15
(M)/(6W + 8B) = X/15
(1/6)/(1/6)(6W + 8B) = X/15
15/6 = X/15
X = (15 * 15)/6
X = 37.5
- Since we cannot have 0.5 days, the answer is rounded up to the nearest whole number, which is 38.
Therefore, the 2 men, 3 women, and 4 boys will complete the work in approximately 38 days.
The closest option to 38 is
Given information:
- The work of 4 men is equal to the work of 6 women.
- The work of 9 women is equal to the work of 12 boys.
- 8 men and 6 women working 8 hours a day complete work in 15 days.
1. Finding the work ratio:
- Let's assume that the work done by 1 man in 1 day is M and the work done by 1 woman in 1 day is W.
- From the given information, we can write the following equations:
4M = 6W (work of 4 men is equal to the work of 6 women)
9W = 12B (work of 9 women is equal to the work of 12 boys)
2. Finding the work done by men and women in 1 day:
- If 8 men and 6 women complete the work in 15 days, we can find the work done by men and women in 1 day.
- Work done by men in 1 day = (8 men * 8 hours) / 15 days = 64M/15
- Work done by women in 1 day = (6 women * 8 hours) / 15 days = 48W/15
3. Finding the work done by 2 men, 3 women, and 4 boys in 1 day:
- We need to find the work done by 2 men, 3 women, and 4 boys in 1 day to determine how many days they will complete the work.
- Work done by 2 men in 1 day = 2M
- Work done by 3 women in 1 day = 3W
- Work done by 4 boys in 1 day = 4B
4. Finding the number of days required:
- Now, we can set up a proportion to find the number of days required:
(Work done by 2 men)/(Work done by 3 women + Work done by 4 boys) = (Number of days required)/(15 days)
(2M)/(3W + 4B) = X/15
- Substituting the values from step 2 and step 3 into the proportion:
(2M)/(3W + 4B) = X/15
(2M)/(3W + 4B) = X/15
(2M)/(3W + 4B) = X/15
(2M)/(3W + 4B) = X/15
- Simplifying the equation:
(8M)/(48W + 64B) = X/15
(M)/(6W + 8B) = X/15
(1/6)/(1/6)(6W + 8B) = X/15
15/6 = X/15
X = (15 * 15)/6
X = 37.5
- Since we cannot have 0.5 days, the answer is rounded up to the nearest whole number, which is 38.
Therefore, the 2 men, 3 women, and 4 boys will complete the work in approximately 38 days.
The closest option to 38 is
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The work of 4 men is equal to the work of 6 women and the work of 9 women is equal to the work of 12 boys. 8 men and 6 women working 8 hours a day complete work is 15 days. In how many days 2 men, 3 women and 4 boys together working 6 hours daily will complete that work?a)40b)45c)60d)48e)50Correct answer is option 'A'. Can you explain this answer?
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