Question

The ratio of the number of men to the number of women on a bus was$2:3$.

At a bus stop,$4$ women got off and the ratio became $4:5$.

A) How many men were on the bus?

B) How many women were on the bus in the end?

Answer 1

Step-1: Given data.

The ratio of the number of men to the number of women on a bus $=2:3.$

At a bus stop, $4$ women got off and the ratio $=4:5.$

Step-2: (A) To find men on the bus:

Assume men are $m$and women are$w.$

As per the problem,

$\frac{m}{w}=\frac{2}{3}$

$\Rightarrow 3m=2w$

$\Rightarrow w=\frac{3m}{2}$……………………………..(i)

$\frac{m}{w-4}=\frac{4}{5}$

$\Rightarrow 5m=4w-16$……………………….(ii)

Substituting equation $\left(i\right)$ in $\left(ii\right)$ we get

$$\begin{gathered} 5m=(4\times \frac{3m}{2})-16 \\ 5m=6m-16 \\ m=16 \end{gathered}$$

Hence, the number of men on the bus are $16$.

Step-3: (B) find the number of women on the bus:

Considering equation $\left(i\right)$ we get,

$$\begin{gathered} w=\frac{3\times 16}{2} \\ w=24 \end{gathered}$$

Hence, the number of women in the bus were $24$.