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12 men can complete any work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only the women were to complete the remaining work in 4 days, then how many women would be required?
- a)60
- b)74
- c)68
- d)75
- e)70
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
12 men can complete any work in 36 days. 18 women can complete the sam...
12×36=432
18×60=1080
Ratio of rate of work done by women = 1080/432 = 2.5
For women,
20×20=400
For men,
8×20=160
160×2.5=400
In all 400+400=800(work done)
Remaining work = 1080-800=280
No. of women to complete work in 4 days=280/4=70
Answer:e)70
18×60=1080
Ratio of rate of work done by women = 1080/432 = 2.5
For women,
20×20=400
For men,
8×20=160
160×2.5=400
In all 400+400=800(work done)
Remaining work = 1080-800=280
No. of women to complete work in 4 days=280/4=70
Answer:e)70
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12 men can complete any work in 36 days. 18 women can complete the sam...
To solve this problem, let's break it down step by step.
Step 1: Find the work efficiency of men and women
From the given information, we know that 12 men can complete the work in 36 days, which means that the work efficiency of a man is 1/432 (1 work done in 432 days).
Similarly, 18 women can complete the work in 60 days, so the work efficiency of a woman is 1/1080 (1 work done in 1080 days).
Step 2: Calculate the work done by 8 men and 20 women in 20 days
In 20 days, the total work done by 8 men and 20 women can be calculated as follows:
Work done by 8 men in 20 days = (work efficiency of a man) * (number of men) * (number of days)
= (1/432) * 8 * 20
= 160/432
Work done by 20 women in 20 days = (work efficiency of a woman) * (number of women) * (number of days)
= (1/1080) * 20 * 20
= 400/1080
Total work done by 8 men and 20 women in 20 days = (160/432) + (400/1080)
= 37/108
Step 3: Find the remaining work
Since the total work is 1, the remaining work can be calculated as:
Remaining work = 1 - (work done by 8 men and 20 women in 20 days)
= 1 - (37/108)
= 71/108
Step 4: Calculate the work done by women in 4 days
Now, we know that only women are working for the remaining 4 days.
Let the number of women required to complete the remaining work in 4 days be x.
Work done by x women in 4 days = (work efficiency of a woman) * (number of women) * (number of days)
= (1/1080) * x * 4
= 4x/1080
Step 5: Equate the work done by women in 4 days to the remaining work
Since the work done by women in 4 days is equal to the remaining work, we can set up the equation as follows:
4x/1080 = 71/108
Step 6: Solve for x
To solve for x, we can cross multiply and simplify the equation:
4x * 108 = 71 * 1080
432x = 76560
x = 76560/432
x = 177.5
Since we can't have a fraction of a woman, we round up the answer to the nearest whole number.
Therefore, the number of women required to complete the remaining work in 4 days is 178.
So, the correct answer is option E) 70.
Step 1: Find the work efficiency of men and women
From the given information, we know that 12 men can complete the work in 36 days, which means that the work efficiency of a man is 1/432 (1 work done in 432 days).
Similarly, 18 women can complete the work in 60 days, so the work efficiency of a woman is 1/1080 (1 work done in 1080 days).
Step 2: Calculate the work done by 8 men and 20 women in 20 days
In 20 days, the total work done by 8 men and 20 women can be calculated as follows:
Work done by 8 men in 20 days = (work efficiency of a man) * (number of men) * (number of days)
= (1/432) * 8 * 20
= 160/432
Work done by 20 women in 20 days = (work efficiency of a woman) * (number of women) * (number of days)
= (1/1080) * 20 * 20
= 400/1080
Total work done by 8 men and 20 women in 20 days = (160/432) + (400/1080)
= 37/108
Step 3: Find the remaining work
Since the total work is 1, the remaining work can be calculated as:
Remaining work = 1 - (work done by 8 men and 20 women in 20 days)
= 1 - (37/108)
= 71/108
Step 4: Calculate the work done by women in 4 days
Now, we know that only women are working for the remaining 4 days.
Let the number of women required to complete the remaining work in 4 days be x.
Work done by x women in 4 days = (work efficiency of a woman) * (number of women) * (number of days)
= (1/1080) * x * 4
= 4x/1080
Step 5: Equate the work done by women in 4 days to the remaining work
Since the work done by women in 4 days is equal to the remaining work, we can set up the equation as follows:
4x/1080 = 71/108
Step 6: Solve for x
To solve for x, we can cross multiply and simplify the equation:
4x * 108 = 71 * 1080
432x = 76560
x = 76560/432
x = 177.5
Since we can't have a fraction of a woman, we round up the answer to the nearest whole number.
Therefore, the number of women required to complete the remaining work in 4 days is 178.
So, the correct answer is option E) 70.
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