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A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there?
  • a)
    17
  • b)
    24
  • c)
    30
  • d)
    22
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A certain number of persons can complete a piece of work in 55 days. I...
Let X be the initial number of men
X × 55 = (X + 6)44
⇒ 55 X = 44 X + 264
⇒ 11 X = 264
⇒ X = 24
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Most Upvoted Answer
A certain number of persons can complete a piece of work in 55 days. I...
Given:
Number of persons required to complete work in 55 days = x
Number of persons required to complete work in (55-11) = 44 days = (x+6)

To find: Original number of persons required to complete work

Solution:
Let us assume that the work is to build a wall.

Step 1:
Let us assume that the wall is 1 meter high and 1 meter wide. The area of the wall is 1 square meter.

Step 2:
Let the number of persons required to build 1 square meter of the wall in 1 day be y
Therefore, the number of persons required to build the entire wall in 1 day would be x*y

Step 3:
The work required to build the wall is 1 square meter. Therefore, the total number of square meters to be built is 1.
The number of persons required to build the entire wall in 55 days would be x*y*55
Similarly, the number of persons required to build the entire wall in 44 days would be (x+6)*y*44

Step 4:
Since the work required is the same, we can equate the two expressions from Step 3.
x*y*55 = (x+6)*y*44

Simplifying the equation, we get:
55x = 44(x+6)
11x = 264
x = 24

Therefore, the original number of persons required to build the wall was 24.

Answer: Option B (24)
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A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there?a)17b)24c)30d)22Correct answer is option 'B'. Can you explain this answer?
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