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B
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Difficulty:
35%
(medium)
Question Stats:
76% (02:23) correct
24%
(02:36)
wrong
based on 151
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A certain number of men can do a piece of work in 18 days working 8 hours a day. If the number of men is increased by 1/3 and the time spent per day is decreased by half, in how many days will the same work be completed?
(A) 24
(B) 27
(C) 30
(D) 33
(E) 31
(A) 24
(B) 27
(C) 30
(D) 33
(E) 31
11 May 2023, 12:31
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Arick
We have a multiplicative relationship between the number of men and time spent.
Given: A certain number of men can do a piece of work in 18 days working 8 hours a day. If the number of men is increased by 1/3, the 'new' number of men can be found out by -
18(1+1/3) = 18 * \(\frac{4}{3}\)
Hence, the number of men increases by a factor of \(\frac{4}{3}\). This action should reduce the time required by a factor of 3/4.
To understand this concept better, let's assume that the number of men were doubled.
Hence, the factor that's applied in this case is 2. If this were the case, with no other change in effect, the time required to complete the task would be \(\frac{1}{2}\) the original time required. This is easily inferable, double the men, half the time required.
Similarly, if the number of men were tripled, the time required would be 1/3rd the original time.
Hence, we can see that the new time required = \(\frac{1}{\text{factor}}\) * old time required
Back to our question -
As the number of men is increased by a factor of \(\frac{4}{3}\), therefore
The number of days required after the change = \(\frac{3}{4}\) * the number of days required before the change
Now, the question doesn't stop here. We are also given that "the time spent per day is decreased by half". Hence. if the time spent is reduced by half, the number of days to complete the piece of work will double. Mathematically,
The number of days required after the change = 2 * The number of days required before the change
Combining both the information
The number of days required after the change = \(\frac{3}{4} \)* 2 * The number of days required before the change
We have multiplied by \(\frac{3}{4}\) to factor in the increase in the number of men and we have multiplied by 2 to factor in the decrease in the time spent per day.
The number of days required after the change= \(\frac{3}{4} \)* 2 * 18
The number of days required = 3 * 9 = 27
Option B
12 May 2023, 01:52
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Given: A certain number of men can do a piece of work in 18 days working 8 hours a day.
Asked: If the number of men is increased by 1/3 and the time spent per day is decreased by half, in how many days will the same work be completed?
Let the number of men be x.
Man-hours needed = x*18*8
Revised men = 4x/3 men
Revised time per day = 4 hours
Number of days needed = x*18*8/(4x/3*4) = x*18*8*3/4x*4 = 27 days
IMO B
Asked: If the number of men is increased by 1/3 and the time spent per day is decreased by half, in how many days will the same work be completed?
Let the number of men be x.
Man-hours needed = x*18*8
Revised men = 4x/3 men
Revised time per day = 4 hours
Number of days needed = x*18*8/(4x/3*4) = x*18*8*3/4x*4 = 27 days
IMO B
