Answer
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Hint: Let us consider that initially there were 100 men in the factory and the planned time is 1 unit. Find the amount of work by the formula ${\text{men}} \times {\text{time = work}}$. Find the required number of men for the new work according to the given relation.
Complete step by step answer:
Let us consider that initially there were 100 men in the factory and the planned time is 1 unit.
We know that the ${\text{men}} \times {\text{time = work}}$
Substitute the value 100 for men and 1 for time , we get work as
$100 \times 1 = 100$
These parameters represent the initial value of the factory.
According to the question, the work in the factory has increased by 50%.
Thus the new work will be initial work + 50% of initial work
The value for initial work was calculated as 100.
Therefore the new work is $100 + 50 = 150$.
We have to complete the work in the previous planned time, that is 1 unit. Therefore the number of men required can be calculated from the formula ${\text{men}} \times {\text{time = work}}$.
${\text{men}} \times {\text{1 = 150}}$
Total men required = 150
However 100 men are already present in the factory. Thus the number of new men required is $150 - 100 = 50$ .
We are given that the efficiency of new men is 25% more than the already present men. Thus, the new men should be hired 25% less.
That is \[50 - 0.25 \times 50 = 40\].
Thus the actual requirement for new men is 40.
Percentage requirement of new men is \[\dfrac{{40}}{{100}} \times 100 = 40\% \], as the initial number of labour was 100.
Thus option C is the correct answer.
Note: The number of times required and the number of men is directly proportional to the amount of work done, that is, ${\text{men}} \times {\text{time = work}}$. Percentage requirement is calculated as 40% in this question, which means the factory requires 40% more men of the total men in the factory.
Complete step by step answer:
Let us consider that initially there were 100 men in the factory and the planned time is 1 unit.
We know that the ${\text{men}} \times {\text{time = work}}$
Substitute the value 100 for men and 1 for time , we get work as
$100 \times 1 = 100$
These parameters represent the initial value of the factory.
According to the question, the work in the factory has increased by 50%.
Thus the new work will be initial work + 50% of initial work
The value for initial work was calculated as 100.
Therefore the new work is $100 + 50 = 150$.
We have to complete the work in the previous planned time, that is 1 unit. Therefore the number of men required can be calculated from the formula ${\text{men}} \times {\text{time = work}}$.
${\text{men}} \times {\text{1 = 150}}$
Total men required = 150
However 100 men are already present in the factory. Thus the number of new men required is $150 - 100 = 50$ .
We are given that the efficiency of new men is 25% more than the already present men. Thus, the new men should be hired 25% less.
That is \[50 - 0.25 \times 50 = 40\].
Thus the actual requirement for new men is 40.
Percentage requirement of new men is \[\dfrac{{40}}{{100}} \times 100 = 40\% \], as the initial number of labour was 100.
Thus option C is the correct answer.
Note: The number of times required and the number of men is directly proportional to the amount of work done, that is, ${\text{men}} \times {\text{time = work}}$. Percentage requirement is calculated as 40% in this question, which means the factory requires 40% more men of the total men in the factory.
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