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It takes six days for three women and two men working together to complete a work. Three men would do the same work five days sooner than nine women. How many times does the output of a man exceed that of a woman?
- a)3 times
- b)4 times
- c)5 times
- d)6 times
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
It takes six days for three women and two men working together to comp...
If 9 women,1 day work= 1/x ---(i)
So 3 men, 1 day work=1/(x-5) ---(ii)
Also given 3 women and 2 men 1 day work= 1/6 ---(iii)
From (i),3 women 1 day work=1/3x
From (ii,2 men 1 day work=2/[3(x-5)]
So (iii) can be represented as, 1/3x + 2/[3(x-5)]= 1/6
Solving x=10
So 1 woman 1 day work=1/(9*10)= 1/90 and
1 man 1 day work=1/3(10-5)= 1/15
Output of a men exceed that of a women = (1/15)/(1/90)= 6 times.
Most Upvoted Answer
It takes six days for three women and two men working together to comp...
Given:
- It takes 6 days for 3 women and 2 men to complete a work.
- 3 men would do the same work 5 days sooner than 9 women.
Objective:
To find out how many times the output of a man exceeds that of a woman.
Assumptions:
- The amount of work done by each person is constant.
- The work done by men and women is independent of each other.
Step-by-step Solution:
1. Let's assume:
Let the work done by a woman in one day be W
Let the work done by a man in one day be M
2. Calculate the work done in 1 day:
From the given information, we can calculate the work done by 3 women and 2 men in 6 days:
Work done by 3 women in 6 days = 3W * 6 = 18W
Work done by 2 men in 6 days = 2M * 6 = 12M
3. Calculate the work done in 1 day by a man and a woman:
Since the work done by men and women is independent, we can set up the following equations:
18W = 12M (From the first statement)
9W = 6M (Dividing both sides by 2)
4. Calculate the work done by 9 women in 1 day:
If 3 men complete the work 5 days sooner than 9 women, it means that the work done by 9 women in 1 day is equal to the work done by 3 men in 6 - 5 = 1 day.
So, the work done by 9 women in 1 day = 3M
5. Find the ratio of work done by a man to that of a woman:
From step 3, we know that 9W = 6M
Dividing both sides by 9, we get:
W = (6/9)M
W = (2/3)M
6. Find the ratio of work done by a man to that of a woman:
From step 4, we know that the work done by 9 women in 1 day = 3M
So, the ratio of work done by a man to that of a woman is:
M / W = M / (2/3)M = 3
7. Conclusion:
The output of a man exceeds that of a woman 3 times. Therefore, the correct answer is option (d) 3 times.
- It takes 6 days for 3 women and 2 men to complete a work.
- 3 men would do the same work 5 days sooner than 9 women.
Objective:
To find out how many times the output of a man exceeds that of a woman.
Assumptions:
- The amount of work done by each person is constant.
- The work done by men and women is independent of each other.
Step-by-step Solution:
1. Let's assume:
Let the work done by a woman in one day be W
Let the work done by a man in one day be M
2. Calculate the work done in 1 day:
From the given information, we can calculate the work done by 3 women and 2 men in 6 days:
Work done by 3 women in 6 days = 3W * 6 = 18W
Work done by 2 men in 6 days = 2M * 6 = 12M
3. Calculate the work done in 1 day by a man and a woman:
Since the work done by men and women is independent, we can set up the following equations:
18W = 12M (From the first statement)
9W = 6M (Dividing both sides by 2)
4. Calculate the work done by 9 women in 1 day:
If 3 men complete the work 5 days sooner than 9 women, it means that the work done by 9 women in 1 day is equal to the work done by 3 men in 6 - 5 = 1 day.
So, the work done by 9 women in 1 day = 3M
5. Find the ratio of work done by a man to that of a woman:
From step 3, we know that 9W = 6M
Dividing both sides by 9, we get:
W = (6/9)M
W = (2/3)M
6. Find the ratio of work done by a man to that of a woman:
From step 4, we know that the work done by 9 women in 1 day = 3M
So, the ratio of work done by a man to that of a woman is:
M / W = M / (2/3)M = 3
7. Conclusion:
The output of a man exceeds that of a woman 3 times. Therefore, the correct answer is option (d) 3 times.
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