a train starts full of passengers and takes 280 more at..., Simplification, General Mathematics

Question:A train starts full of passengers and takes `280` more .At the seceond station,it drops one half of the new total anf takes `12`more .On arriving at the third station ,it is found to have `248`passengers .The number of passsengers in the begining was :

A `156` 
B `288` 
C `564` 
D `608`

/94

+ AnswerB

+ ExplanationLet the number of passengers in the begining be x,

After 1st station ,passengers 

`= (x - x/3) + 280`

`= ((2x)/3 + 280)`

After 2nd starion ,passengers 

`= ((2x)/3 +280) - 1/2 ((2x)/3 + 280) + 12`

`:. 1/2((2x)/3 + 280) + 12= 248`

`or (2x)/3 + 280`

`= 2 xx 236`

`or (2x)/3 = 192`

`:. x = (192 xx 3/2) = 288`.

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