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$30$ % passenger from train got down at station $A,$ $70$ % of the remaining got down at station $B,$ If there are still $1050$ passenger in the train, how many passenger were there before station $A,$ provided no one boarded the train at station $A$ and $B$ ?

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Solution

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Let us assume that no one boarded the train at station at A and B.
Let,
total passenger before station A = x
30% passengers from train got down at station A.
Therefore total number pf passengers got down at station A = 30% of x = $begin mathsize 16px style fraction numerator 30 straight x over denominator 100 end fraction space equals space space fraction numerator 3 straight x over denominator 10 end fraction end style$
$begin mathsize 16px style rightwards double arrow Remaining space passengers space space equals straight x space minus space fraction numerator 3 straight x over denominator 10 end fraction equals space fraction numerator 10 straight x space minus space 3 straight x over denominator 10 space end fraction space equals space fraction numerator 7 straight x over denominator 10 end fraction end style$
70% passengers from train got down at station B.
Therefore total number pf passengers got down at station B = $begin mathsize 16px style equals 70 percent sign space of space space fraction numerator 7 straight x over denominator 10 end fraction space equals fraction numerator 70 space over denominator 100 end fraction space cross times space fraction numerator 7 straight x over denominator 10 end fraction equals space space fraction numerator 49 straight x over denominator 100 end fraction end style$
$begin mathsize 16px style rightwards double arrow Remaining space passengers space space equals fraction numerator 7 straight x over denominator 10 end fraction space minus space fraction numerator 49 straight x over denominator 100 end fraction equals space fraction numerator 70 straight x space minus space 49 straight x over denominator 100 space end fraction space equals space fraction numerator 21 straight x over denominator 10 end fraction space space space space space end style$
Given that there are still 1050 passengers in the train.
$begin mathsize 16px style rightwards double arrow fraction numerator 21 straight x over denominator 100 end fraction space space equals space 1050 rightwards double arrow straight x space equals space 5000 end style$
Therefore the total number of passengers before station A are 5000.

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