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A certain number of men can finish a piece of work in 10 days. If however there were 10 men less it will take 10 days more for the work to be finished. How many men were there originally?
- a)110 men
- b)130 men
- c)100 men
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A certain number of men can finish a piece of work in 10 days. If howe...
Given information:
- A certain number of men can finish a piece of work in 10 days.
- If there were 10 men less, it will take 10 days more for the work to be finished.
To find: How many men were there originally?
Solution:
Let's assume that the original number of men required to finish the work is x.
According to the given information, we can form two equations:
- Equation 1: Work done by x men in 10 days = 1 (complete work)
- Equation 2: Work done by (x - 10) men in 20 days = 1 (complete work)
To solve for x, we can use these equations:
- Multiply equation 1 by (x - 10) to get rid of x and form a new equation.
- Multiply equation 2 by x to get rid of (x - 10) and form another equation.
- Equate the two new equations and solve for x.
Here's the calculation:
- Equation 1: Work done by x men in 10 days = 1
=> Work done by 1 man in 1 day = 1/(10x)
- Equation 2: Work done by (x - 10) men in 20 days = 1
=> Work done by 1 man in 1 day = 1/(20(x - 10))
- Multiplying equation 1 by (x - 10):
(x - 10) * Work done by 1 man in 1 day * 10 = 1
(x - 10)/(10x) = 1/10
x - 10 = x/10
10x - 100 = x
x = 100
Therefore, the original number of men required to finish the work is 100.
Answer: Option A (110 men) is incorrect. Option A (100 men) is the correct answer.
- A certain number of men can finish a piece of work in 10 days.
- If there were 10 men less, it will take 10 days more for the work to be finished.
To find: How many men were there originally?
Solution:
Let's assume that the original number of men required to finish the work is x.
According to the given information, we can form two equations:
- Equation 1: Work done by x men in 10 days = 1 (complete work)
- Equation 2: Work done by (x - 10) men in 20 days = 1 (complete work)
To solve for x, we can use these equations:
- Multiply equation 1 by (x - 10) to get rid of x and form a new equation.
- Multiply equation 2 by x to get rid of (x - 10) and form another equation.
- Equate the two new equations and solve for x.
Here's the calculation:
- Equation 1: Work done by x men in 10 days = 1
=> Work done by 1 man in 1 day = 1/(10x)
- Equation 2: Work done by (x - 10) men in 20 days = 1
=> Work done by 1 man in 1 day = 1/(20(x - 10))
- Multiplying equation 1 by (x - 10):
(x - 10) * Work done by 1 man in 1 day * 10 = 1
(x - 10)/(10x) = 1/10
x - 10 = x/10
10x - 100 = x
x = 100
Therefore, the original number of men required to finish the work is 100.
Answer: Option A (110 men) is incorrect. Option A (100 men) is the correct answer.
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A certain number of men can finish a piece of work in 10 days. If however there were 10 men less it will take 10 days more for the work to be finished. How many men were there originally?a)110 menb)130 menc)100 mend)none of theseCorrect answer is option 'A'. Can you explain this answer?
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