Question

If $\dfrac{7}{{12}}$ of the passengers in a ship are adults, the rest are children and $\dfrac{2}{5}$ of the adults are men then find the ratio of the number of women to the number of children.
(A) $5:12$
(B) $14:25$
(C) $21:25$
(D) $4:25$

Answer 1

Hint: : In this problem, to find the required ratio first we will assume that the total number of passengers in a ship is $x$. Then, we will use the given data to find the number of women and number of children. Then, we will find the ratio.

Complete step-by-step answer:
Let us assume that the total number of passengers is $x$ in a ship. It is given that $\dfrac{7}{{12}}$ of total passengers are adults. So, we can write the number of adult passengers $ = \dfrac{7}{{12}}$. It is also given that the rest are children. So, we can write number of children passengers $ = x - \dfrac{{7x}}{{12}} = \dfrac{{5x}}{{12}} \cdots \cdots \left( 1 \right)$ because the total number of passengers is $x$. Also it is given that $\dfrac{2}{5}$ of that adult passengers are men. So, we can write number of men passengers $ = \dfrac{{2x}}{5}$ and number of women passengers $ = x - \dfrac{{2x}}{5} = \dfrac{{3x}}{5}$ and
number of adult women passengers $ = \dfrac{7}{{12}}\left( {\dfrac{{3x}}{5}} \right) = \dfrac{{7x}}{{20}} \cdots \cdots \left( 2 \right)$.
From $\left( 1 \right)$ and $\left( 2 \right)$, we can find the required ratio. That is, ratio of the number of women to the number of children is given by $\dfrac{{\dfrac{{7x}}{{20}}}}{{\dfrac{{5x}}{{12}}}} = \dfrac{7}{{20}} \times \dfrac{{12}}{5} = \dfrac{{21}}{{25}}$ or $21:25$.
Hence, the required ratio is $21:25$.
So, the correct answer is “Option C”.

Note: in this type of problems, we are comparing two quantities and this comparison is called the ratio. The ratio is denoted by using the symbol $:$. Remember that we can compare two quantities only if they are in the same unit.