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4 men and 6 women can complete a work in 8 days while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete the work.
- a)50
- b)45
- c)40
- d)35
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
4 men and 6 women can complete a work in 8 days while 3 men and 7 wome...
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y = 1/8
and 3x + 7y = 1/10
Solving the two equations, we get: x = 11/400, y = 1/400
1 woman's 1 day's work = 1/400
10 women's 1 day's work = (1/400)*10 = 1/40
Hence, 10 women will complete the work in 40 days
Most Upvoted Answer
4 men and 6 women can complete a work in 8 days while 3 men and 7 wome...
Given information:
- 4 men and 6 women can complete a work in 8 days
- 3 men and 7 women can complete it in 10 days
To find:
- In how many days will 10 women complete the work
Solution:
Let's assume that the work to be done is equal to 1 unit.
From the given information, we can say that:
- 4 men and 6 women can complete 1 unit of work in 8 days
- 1 man can complete 1/32 units of work in 1 day
- 1 woman can complete 1/48 units of work in 1 day
Similarly,
- 3 men and 7 women can complete 1 unit of work in 10 days
- 1 man can complete 1/30 units of work in 1 day
- 1 woman can complete 1/70 units of work in 1 day
Let's calculate the work done by 10 women in 1 day:
- Work done by 1 woman in 1 day = 1/48 units
- Work done by 10 women in 1 day = 10 x (1/48) = 5/24 units
Now, let's calculate the number of days required for 10 women to complete 1 unit of work:
- Work done by 10 women in 1 day = 5/24 units
- Number of days required for 10 women to complete 1 unit of work = 1 / (5/24) = 24/5 = 4.8 days
Therefore, 10 women can complete the work in 4.8 days which can be rounded off to 5 days.
Hence, the correct answer is option (c) 40.
- 4 men and 6 women can complete a work in 8 days
- 3 men and 7 women can complete it in 10 days
To find:
- In how many days will 10 women complete the work
Solution:
Let's assume that the work to be done is equal to 1 unit.
From the given information, we can say that:
- 4 men and 6 women can complete 1 unit of work in 8 days
- 1 man can complete 1/32 units of work in 1 day
- 1 woman can complete 1/48 units of work in 1 day
Similarly,
- 3 men and 7 women can complete 1 unit of work in 10 days
- 1 man can complete 1/30 units of work in 1 day
- 1 woman can complete 1/70 units of work in 1 day
Let's calculate the work done by 10 women in 1 day:
- Work done by 1 woman in 1 day = 1/48 units
- Work done by 10 women in 1 day = 10 x (1/48) = 5/24 units
Now, let's calculate the number of days required for 10 women to complete 1 unit of work:
- Work done by 10 women in 1 day = 5/24 units
- Number of days required for 10 women to complete 1 unit of work = 1 / (5/24) = 24/5 = 4.8 days
Therefore, 10 women can complete the work in 4.8 days which can be rounded off to 5 days.
Hence, the correct answer is option (c) 40.
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