Question

Out of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the number of persons to that of women.

Answer 1

Hint: We have the number of persons working and the number of men. So, we can find the number of women by subtracting the number of men from the number of persons working. Then we find the required ratio by dividing the number of persons with the number of women.

Complete step by step answer:

It is given that 72 persons are working. Let t be the total number of persons working.
$ \Rightarrow t = 72$
It is also given that 28 men are working in the office. Let x be the number of men.
$ \Rightarrow x = 28$
Let y be the number of women. Then the number of women working is given by subtracting the number of men from the number of persons working in the office.
\[ \Rightarrow y = t - x\]
On substituting the values, we get,
\[ \Rightarrow y = 72 - 28\]
On simplification we get,
\[ \Rightarrow y = 44\]
Now we have the number of women as 44.
We need to find the ratio of the number of persons to that of women. For that, we can divide the number of workers by the number of women.
$ \Rightarrow Ratio = \dfrac{t}{y}$
On substituting the values, we get,
$ \Rightarrow Ratio = \dfrac{{72}}{{44}}$
On further simplification, we get,
$ \Rightarrow Ratio = \dfrac{{18}}{{11}}$
Therefore, the required ratio is $18:11$.

Note: Alternate solution to this problem is given by,
The number of workers is 72 and the number of men is 28.
Now the ratio of men to the number of workers is $\dfrac{{28}}{{72}} = \dfrac{7}{{18}}$ .
Then the ratio of women to the number of workers is given by, $1 - \dfrac{7}{{18}} = \dfrac{{18 - 7}}{{18}} = \dfrac{{11}}{{18}}$ .
The required ratio is the number of persons to that of women. So we can take the reciprocal.
$ \Rightarrow Ratio = \dfrac{{18}}{{11}}$
Therefore, the required ratio is $18:11$