Bus!

women be x, men be 2x so,in city Y , we have :(2x-10)=(x+5) or x=15, Therefore,total no. of passengers in the beginning=(x+2x)=3x=45.

@city X

women=1/2 men

x=women

2x=men

@city Y

2x-10=men

x+5=women

2x-10=x+5

2x-x=5+10; thus x=15

Initial no. of passengers: women+men@city X =x+2x=15+(2x15) =45 persons:)

The logic is like this:

$\boxed{W=\frac{1}{2} M}$

$\boxed{W+5=M-10}$

Do the magic:

( $\frac{1}{2}$ M)+5 = M-10 $\Rightarrow$ $\frac{1}{2}$ M=15 $\Rightarrow$ $\boxed{M=30}$

W= $\frac{30}{2}$ $\Rightarrow$ $\boxed{W=15}$

So the summary of the passengers originally is 30 + 15 = $\boxed{45}$