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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...
Given information:
- Total work to be completed in 50 days.
- Only half of the work is done in 30 days.
- An additional 20 men were joined to complete the work on time.
To solve this problem, we can use the concept of work and time.
Let's assume that initially, x men were put to work.
So, the total work done by x men in 30 days = (1/2) of the total work.
Now, we need to find out how many men are required to complete the remaining half of the work in 20 days.
Let the required number of men be y.
Using the formula of work and time, we can write:
Work done by x men in 30 days + Work done by y men in 20 days = Total work
[(1/2) of total work] + Work done by y men in 20 days = Total work
Work done by y men in 20 days = (1/2) of total work
Now, we can use the formula of work and men to find out the relationship between x and y.
Work done by x men in 30 days = Work done by y men in 20 days
x * 30 * (1/2) = y * 20 * (1/2)
x = (2/3) y
Now, we can substitute the value of x in terms of y in the above equation:
(2/3) y * 30 * (1/2) + y * 20 * (1/2) = Total work
y * 25 = Total work
To complete the total work in 50 days, the required number of men are:
y = Total work / 25
y = 2 * Total work / 50
y = 2
This means that initially, x = (2/3) y = (2/3) * 2 = 4/3 men were put to work.
But we know that the number of men should be a whole number. So, we need to round up the value of x to the nearest whole number.
Hence, the initial number of men put to work = 2 men * 3/4 = 6/4 = 1.5 * 20 = 30 men.
Therefore, the correct option is (c) 40 men.
- Total work to be completed in 50 days.
- Only half of the work is done in 30 days.
- An additional 20 men were joined to complete the work on time.
To solve this problem, we can use the concept of work and time.
Let's assume that initially, x men were put to work.
So, the total work done by x men in 30 days = (1/2) of the total work.
Now, we need to find out how many men are required to complete the remaining half of the work in 20 days.
Let the required number of men be y.
Using the formula of work and time, we can write:
Work done by x men in 30 days + Work done by y men in 20 days = Total work
[(1/2) of total work] + Work done by y men in 20 days = Total work
Work done by y men in 20 days = (1/2) of total work
Now, we can use the formula of work and men to find out the relationship between x and y.
Work done by x men in 30 days = Work done by y men in 20 days
x * 30 * (1/2) = y * 20 * (1/2)
x = (2/3) y
Now, we can substitute the value of x in terms of y in the above equation:
(2/3) y * 30 * (1/2) + y * 20 * (1/2) = Total work
y * 25 = Total work
To complete the total work in 50 days, the required number of men are:
y = Total work / 25
y = 2 * Total work / 50
y = 2
This means that initially, x = (2/3) y = (2/3) * 2 = 4/3 men were put to work.
But we know that the number of men should be a whole number. So, we need to round up the value of x to the nearest whole number.
Hence, the initial number of men put to work = 2 men * 3/4 = 6/4 = 1.5 * 20 = 30 men.
Therefore, the correct option is (c) 40 men.
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Community 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
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