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If 2 men or 5 women can complete a work in 15 days, then in how many days 4 men and 5 women will complete the same work?
- a)7
- b)12
- c)8
- d)5
- e)10
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If 2 men or 5 women can complete a work in 15 days, then in how many d...
D) 5
Explanation: 2 m or 5 w 4m + 5w Cross multiply and put in denominator Days = 15*2*5/ [2*5 +5*4]
Explanation: 2 m or 5 w 4m + 5w Cross multiply and put in denominator Days = 15*2*5/ [2*5 +5*4]
Most Upvoted Answer
If 2 men or 5 women can complete a work in 15 days, then in how many d...
Let's assume that the work to be completed is represented by the variable "W".
Given:
2 men can complete the work in 15 days.
So, in 1 day, 2 men can complete 1/15th of the work.
Therefore, the work done by 1 man in 1 day is 1/(2*15) = 1/30th of the work.
Similarly,
5 women can complete the work in 15 days.
So, in 1 day, 5 women can complete 1/15th of the work.
Therefore, the work done by 1 woman in 1 day is 1/(5*15) = 1/75th of the work.
To find the number of days required for 4 men and 5 women to complete the work, we need to calculate the combined work done by them in 1 day.
Let's calculate the work done by 4 men in 1 day:
Work done by 1 man in 1 day = 1/30th of the work
Work done by 4 men in 1 day = 4 * (1/30) = 2/15th of the work
Now, let's calculate the work done by 5 women in 1 day:
Work done by 1 woman in 1 day = 1/75th of the work
Work done by 5 women in 1 day = 5 * (1/75) = 1/15th of the work
Therefore, the combined work done by 4 men and 5 women in 1 day is:
(2/15) + (1/15) = 3/15 = 1/5th of the work.
So, in 1 day, 4 men and 5 women can complete 1/5th of the work.
To find the number of days required to complete the entire work, we can set up the following equation:
(1/5) * D = 1
Where D represents the number of days required.
Simplifying the equation, we get:
D = 5
Therefore, 4 men and 5 women will complete the same work in 5 days.
Hence, the correct answer is option D.
Given:
2 men can complete the work in 15 days.
So, in 1 day, 2 men can complete 1/15th of the work.
Therefore, the work done by 1 man in 1 day is 1/(2*15) = 1/30th of the work.
Similarly,
5 women can complete the work in 15 days.
So, in 1 day, 5 women can complete 1/15th of the work.
Therefore, the work done by 1 woman in 1 day is 1/(5*15) = 1/75th of the work.
To find the number of days required for 4 men and 5 women to complete the work, we need to calculate the combined work done by them in 1 day.
Let's calculate the work done by 4 men in 1 day:
Work done by 1 man in 1 day = 1/30th of the work
Work done by 4 men in 1 day = 4 * (1/30) = 2/15th of the work
Now, let's calculate the work done by 5 women in 1 day:
Work done by 1 woman in 1 day = 1/75th of the work
Work done by 5 women in 1 day = 5 * (1/75) = 1/15th of the work
Therefore, the combined work done by 4 men and 5 women in 1 day is:
(2/15) + (1/15) = 3/15 = 1/5th of the work.
So, in 1 day, 4 men and 5 women can complete 1/5th of the work.
To find the number of days required to complete the entire work, we can set up the following equation:
(1/5) * D = 1
Where D represents the number of days required.
Simplifying the equation, we get:
D = 5
Therefore, 4 men and 5 women will complete the same work in 5 days.
Hence, the correct answer is option D.
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