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A piece of work has to be completed in 50 days, a number of men are employed but it is found that only half of the work is done in 30 days, then an additional 20 men were joined to complete the work on time. How many men initially put to work?
- a)30
- b)35
- c)40
- d)45
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A piece of work has to be completed in 50 days, a number of men are em...
suppose Initially X men get employed. Half work is done in 30 days it means full work will be done by X men in 60 days. Now,
Work done = 1/2 = [20*(x + 20)]/60X
X = 40
Work done = 1/2 = [20*(x + 20)]/60X
X = 40
Most Upvoted Answer
A piece of work has to be completed in 50 days, a number of men are em...
Let's assume that the total work required to be completed is 1 unit.
**Work Done in 30 Days:**
It is given that only half of the work is done in 30 days. So, the work done in 30 days is (1/2) unit.
**Work Remaining:**
The remaining work to be completed after 30 days is (1 - 1/2) = 1/2 unit.
**Work Completed by Additional Men:**
It is given that the work needs to be completed in 50 days. So, the remaining work of 1/2 unit must be completed in the next 20 days.
Let's assume that the number of men initially put to work was x.
**Work Done by x Men in 30 Days:**
The work done by x men in 30 days is (1/2) unit.
**Work Done by x Men in 50 Days:**
The work done by x men in 50 days is (1 unit).
**Work Done by x Men in 20 Days:**
The work done by x men in 20 days is (1/50) * 20 = 2/5 unit.
**Additional Work Done by 20 Men in 20 Days:**
The additional work done by 20 men in 20 days is (1/50) * 20 = 2/5 unit.
**Total Work Done by x Men and 20 Men:**
The total work done by x men and 20 men in 20 days is (2/5) + (2/5) = 4/5 unit.
**Remaining Work:**
The remaining work after 20 days is (1/2) - (4/5) = 1/10 unit.
**Work Done by x Men in 50 Days:**
The work done by x men in 50 days is (1 unit).
**Equating the Work Done by x Men:**
The work done by x men in 50 days is equal to the remaining work of 1/10 unit.
Therefore, (1 unit) = (1/10 unit) * 50,
which gives x = 5.
Hence, the number of men initially put to work is 5.
Therefore, the correct answer is option C) 40.
**Work Done in 30 Days:**
It is given that only half of the work is done in 30 days. So, the work done in 30 days is (1/2) unit.
**Work Remaining:**
The remaining work to be completed after 30 days is (1 - 1/2) = 1/2 unit.
**Work Completed by Additional Men:**
It is given that the work needs to be completed in 50 days. So, the remaining work of 1/2 unit must be completed in the next 20 days.
Let's assume that the number of men initially put to work was x.
**Work Done by x Men in 30 Days:**
The work done by x men in 30 days is (1/2) unit.
**Work Done by x Men in 50 Days:**
The work done by x men in 50 days is (1 unit).
**Work Done by x Men in 20 Days:**
The work done by x men in 20 days is (1/50) * 20 = 2/5 unit.
**Additional Work Done by 20 Men in 20 Days:**
The additional work done by 20 men in 20 days is (1/50) * 20 = 2/5 unit.
**Total Work Done by x Men and 20 Men:**
The total work done by x men and 20 men in 20 days is (2/5) + (2/5) = 4/5 unit.
**Remaining Work:**
The remaining work after 20 days is (1/2) - (4/5) = 1/10 unit.
**Work Done by x Men in 50 Days:**
The work done by x men in 50 days is (1 unit).
**Equating the Work Done by x Men:**
The work done by x men in 50 days is equal to the remaining work of 1/10 unit.
Therefore, (1 unit) = (1/10 unit) * 50,
which gives x = 5.
Hence, the number of men initially put to work is 5.
Therefore, the correct answer is option C) 40.
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A piece of work has to be completed in 50 days, a number of men are employed but it is found that only half of the work is done in 30 days, then an additional 20 men were joined to complete the work on time. How many men initially put to work?a)30b)35c)40d)45e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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