Question

1/7 th of the passenger of a train were children,3/5 th of the passenger were gents and the rest were ladies.If the number of ladies in the train was 360. Find the total number of passengers in the train.

Answer 1

Suppose the total number of passengers in the train is x.
So, number of children = $\frac{1}{7}$th of total passenger = $\frac{x}{7}$
Number of gents = $\frac{3}{5}$ of total passenger = $\frac{3x}{5}$
Then number of ladies = Total passenger - (number of children + number of gents)
$$\begin{gathered} \Rightarrow 360=x-\left(\frac{x}{7}+\frac{3x}{5}\right) \\ \Rightarrow 360=x-\left(\frac{5x+21x}{35}\right) \\ \Rightarrow 360=x-\frac{26x}{35} \\ \Rightarrow 360=\frac{35x-26x}{35} \\ \Rightarrow \frac{9x}{35}=360 \\ \Rightarrow x=\frac{360\times 35}{9}=1400 \end{gathered}$$
Therefore total number of passengers in the train is 1400.