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.

*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)

$\Rightarrow 360=x-\left(\frac{x}{7}+\frac{3x}{5}\right)\phantom{\rule{0ex}{0ex}}\Rightarrow 360=x-\left(\frac{5x+21x}{35}\right)\phantom{\rule{0ex}{0ex}}\Rightarrow 360=x-\frac{26x}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow 360=\frac{35x-26x}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{9x}{35}=360\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{360\times 35}{9}=1400$

Therefore total number of passengers in the train is 1400.

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