Answer

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**Hint:**In this particular problem, we firstly will find the total numbers of women and men separately. Then by using the given data, we will find out how many people are married and how many of them are not. Then after solving the problem, we will get the maximum number of women who could be unmarried, in the room.

**Complete step-by-step answer:**

The total number of people in the room = $120$

As, It is given that, Number of women $ = \dfrac{3}{5}$ of $120 = 72$

Hence number of men in the room = Total number of people – number of women in the room

\[ \Rightarrow \]$ 120 - 72$

\[ \Rightarrow \]$ 48$

Hence, number of men in the room$ = 48$

Now, it is also given in the problem that number of people married$ = \dfrac{2}{3}$ of $120 = 80$

Hence, number of people unmarried $ = 120 - 80$

\[ \Rightarrow \]$ 40$

Suppose all the men in the room are married i.e. $48$.

So, number of women married = Total number of married people – number of married men

\[ \Rightarrow \]$ 80 - 48$

\[ \Rightarrow \]$ 32$

Hence, the number of women married $ = 32$.

So, number of women unmarried= Total number of women in the room – number of women married

\[ \Rightarrow \]$ 72 - 32$

\[ \Rightarrow \]$ 40$

**Hence, the maximum number of women in the room that could be unmarried is $40$.**

**Note:**In this problem, the total number of people present in the room was given to be $120$ and some fractions were given for the number of women and the number of people that are married out of $120$ people in the room.

Fractions are the Terms having numerator and the denominator e.g. $\dfrac{3}{{16}},\dfrac{2}{9}$ etc.

In the given problem, $\dfrac{3}{5}$ of the total people were given to be women.i.e. $\dfrac{3}{5} \times 120 = 72$

$\dfrac{2}{3}$ of the total people were given to be married i.e. $\dfrac{2}{3} \times 120 = 80$

To find the maximum number of women unmanned, we needed to find the minimum number of women married. So, we found the maximum number of men married that was all the men present in the room.

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