Question

In a factory, women are 35 % of all the workers, the rest of the workers being men. The number of men exceeds that of women by 252. Find the total number of workers in the factory.

Answer 1

Hint: We are given women are 35 % of all the workers. We will first assume the number of women as x, then we will find the number of women workers as 35 % of x that is \[\dfrac{35}{100}\] of x. Then once we have the number of women workers, we will subtract it from the total workers (x) to get the number of men workers. At last, as their difference is 252, we will subtract the men and women workers and solve for x.

Complete step-by-step answer:
We are given that in a factory, 35 % of workers are women and the others are men. Also, we have men who are more than women by 252. We are asked to find the total workers in the factory. Let us start with the assumption that the total workers of the factory are x in number.
Now, we have women in the factory who are 35 % of the total workers. So,
Number of women = 35 % of total workers
As total workers = x, so,
Number of women = 35 % of x
\[\Rightarrow \dfrac{35}{100}\text{ of }x\]
Therefore,
\[\text{Number of women}=\dfrac{35x}{100}\]
Now, as women are 35 % and the rest are men. So,
\[35\%\text{ of women}=\dfrac{35x}{100}\text{ women}\]
Now,
The number of men = Total workers – Number of Women
So, the total number of men will be
\[\text{Total number of men}=x-\dfrac{35x}{100}\]
Simplifying, we get,
\[\Rightarrow \text{Total number of men}=\dfrac{100x-35x}{100}\]
\[\Rightarrow \text{Total number of men}=\dfrac{65x}{100}\]
Now, we have that the men are just 252 more than the women in the factory. So, it means the difference between the number of men and women is 252. So,
Number of men – Number of women = 252
\[\Rightarrow \dfrac{65x}{100}-\dfrac{35x}{100}=252\]
On simplifying, we get,
\[\Rightarrow \dfrac{30x}{100}=252\]
On cross multiplying, we get,
\[\Rightarrow x=\dfrac{252\times 100}{30}\]
After simplifying, we get,
\[\Rightarrow x=840\]
So, the total workers in the factory are 840.

Note: To find the number of men, we can first find the percentage of men and then calculate like, as women are only 35 %. So, men will be 100 – % of women.
Percentage of men workers = 100 – 35 = 65 %
Also, remember when the denominator is the same, then we just subtract the numerator only and keep the denominator as it is. That’s how we get,
\[\Rightarrow \dfrac{5x}{100}-\dfrac{35x}{100}=\dfrac{30x}{100}\]