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A contractor undertakes to do a job in 18 days. He employees certain number of men, but 12 of them being absent from the very first day, the rest can complete the work in 30 days. The number of men originally employed?
  • a)
    20
  • b)
    25
  • c)
    30
  • d)
    40
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A contractor undertakes to do a job in 18 days. He employees certain n...
Answer – c) 30 Explanation : Let ‘m’ men are originally employed m*18 = (m -12)*30 m = 30
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Most Upvoted Answer
A contractor undertakes to do a job in 18 days. He employees certain n...
Easy one-
let total work= total man days =LCM(18,30)=90 man days or 90 work.
so to accomplish 90 works 5 men to be done for 18 days = 18*5=90 works
and to complete 90 works in 30 days,3 men to be done in a day.

so difference in men is 2 ,but as per qn 12 men were less. and 12 is 6 times 2.so multiply 6 with everything in the entire equation.but we need total men for 18 days .so 5 men * 6= 30 men , which is actual expected men and so the answer.and actually present men were 30-12=18.

ANS IS 30 MEN.
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A contractor undertakes to do a job in 18 days. He employees certain n...
Given:
- A contractor undertakes to do a job in 18 days.
- He employs a certain number of men, but 12 of them being absent from the very first day.
- The rest can complete the work in 30 days.

To find: The number of men originally employed.

Solution:
Let's assume that the total work to be done is 1 unit (for simplicity).

Let's say the number of men originally employed is x.

Work done by x men in 1 day = 1/18 (since they can complete the work in 18 days)

Work done by 1 man in 1 day = (1/18)/x = 1/18x

Let's say the number of men who were present from the first day is y (out of x men).

So the work done by y men in 1 day = y/18x

Since the remaining men (x-y) can complete the work in 30 days,

Work done by x-y men in 1 day = 1/(30(x-y))

Total work done by all men in a day = y/18x + 1/(30(x-y))

We know that if all x men were present, they could have completed the work in 18 days. So,

Work done by x men in 1 day = 1/18

Work done by 1 man in 1 day = 1/18x (as derived earlier)

Total work done by all x men in a day = x/18x = 1/18

We can equate the above two equations to get:

y/18x + 1/(30(x-y)) = 1/18

Simplifying the equation, we get:

y/2x + 1/(5(x-y)) = 1/3

Multiplying both sides by 30x(x-y), we get:

15y(x-y) + 6x(x-y) = 10x^2

Simplifying further, we get:

10x^2 - 21xy + 6y^2 = 0

We need to find the value of x.

We know that x > y (since 12 men were absent from the first day)

We can factorize the above equation as:

(10x - 3y)(x - 2y) = 0

Since x > y, we can ignore the second factor and consider only the first factor:

10x - 3y = 0

10x = 3y

y = (10/3)x

Since y is an integer, x should be a multiple of 3 and a factor of 10.

The possible values of x are: 3, 6, 10, 15, 30, 5, 20, 25, 40, 50

Out of these, the only value that satisfies the equation y = (10/3)x is x = 30.

Therefore, the number of men originally employed is 30.

Answer: (c) 30.
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A contractor undertakes to do a job in 18 days. He employees certain number of men, but 12 of them being absent from the very first day, the rest can complete the work in 30 days. The number of men originally employed?a)20b)25c)30d)40e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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