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x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men is
- a)6
- b)10
- c)12
- d)15
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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x number of men can finish a piece of work in 30 days. If there were 6...
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x number of men can finish a piece of work in 30 days. If there were 6...
Given:
- x men can finish a piece of work in 30 days.
- If there were 6 men more, the work could be finished in 10 days less.
To find:
- The original number of men.
Solution:
Let's assume the original number of men is 'n'.
Step 1: Determining the work rate
- In 30 days, x men can complete the work.
- Therefore, the work rate of x men is 1/30 per day.
- Let's calculate the work rate of 1 man per day, which would be (1/30) / x = 1/(30x).
Step 2: Determining the new work rate
- If there were 6 men more, the work could be finished in 10 days less.
- This means that (n + 6) men can complete the work in 30 - 10 = 20 days.
- Therefore, the work rate of (n + 6) men is 1/20 per day.
- Let's calculate the work rate of 1 man per day, which would be (1/20) / (n + 6) = 1/(20(n + 6)).
Step 3: Equating the work rates
- Since the work done by both groups of men is the same, the work rates can be equated.
- 1/(30x) = 1/(20(n + 6))
Step 4: Solving the equation
- To simplify the equation, we can cross-multiply.
- 20(n + 6) = 30x
- Simplifying further, we get:
- 20n + 120 = 30x
- 20n = 30x - 120
- 2n = 3x - 12
Step 5: Substituting values to find the original number of men
- Since the answer options are given in terms of individual men, we can substitute some values to find the original number of men.
- Let's try n = 12:
- 2(12) = 3x - 12
- 24 = 3x - 12
- 36 = 3x
- x = 12
- Therefore, the original number of men is 12.
Hence, the correct answer is option 'C' (12).
- x men can finish a piece of work in 30 days.
- If there were 6 men more, the work could be finished in 10 days less.
To find:
- The original number of men.
Solution:
Let's assume the original number of men is 'n'.
Step 1: Determining the work rate
- In 30 days, x men can complete the work.
- Therefore, the work rate of x men is 1/30 per day.
- Let's calculate the work rate of 1 man per day, which would be (1/30) / x = 1/(30x).
Step 2: Determining the new work rate
- If there were 6 men more, the work could be finished in 10 days less.
- This means that (n + 6) men can complete the work in 30 - 10 = 20 days.
- Therefore, the work rate of (n + 6) men is 1/20 per day.
- Let's calculate the work rate of 1 man per day, which would be (1/20) / (n + 6) = 1/(20(n + 6)).
Step 3: Equating the work rates
- Since the work done by both groups of men is the same, the work rates can be equated.
- 1/(30x) = 1/(20(n + 6))
Step 4: Solving the equation
- To simplify the equation, we can cross-multiply.
- 20(n + 6) = 30x
- Simplifying further, we get:
- 20n + 120 = 30x
- 20n = 30x - 120
- 2n = 3x - 12
Step 5: Substituting values to find the original number of men
- Since the answer options are given in terms of individual men, we can substitute some values to find the original number of men.
- Let's try n = 12:
- 2(12) = 3x - 12
- 24 = 3x - 12
- 36 = 3x
- x = 12
- Therefore, the original number of men is 12.
Hence, the correct answer is option 'C' (12).
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x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men isa)6b)10c)12d)15e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men isa)6b)10c)12d)15e)None of theseCorrect answer is option 'C'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men isa)6b)10c)12d)15e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men isa)6b)10c)12d)15e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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