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# Find a fraction which becomes (1/2) when 1 subtracted from the numerator and 2 is added to the denominator, and the fraction becomes (1/3) when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

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This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Question Number 22 Exercise 3E of RS Aggarwal Solution
Here you have to Find a fraction which becomes (1/2) when a number is subtracted from the numerator and a number is added to the denominator, and the fraction becomes (1/3) when a number is subtracted from the numerator and a number is subtracted from the denominator.
you have to find the fraction.

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1. Let the numerator be cans denominator be y
fraction=x/y
x-1/y+2=1/2
2x-2=y+2
2x-y=4…. ..(1)
x-7/y-2=1/3
3x-21=y-2
3x-y=19……..(2)
2x-y=4
3x-y=19
– + –
________
-x=-15
x=15
putx=15 in equation (1)
2x-y=4
2×15-y=4
30-y=4
-y=4-30
-y=-26
y=26
thus, the required fraction is 15/26

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