In this Question if given number added to the numerator of a fraction, it reduces to (1/2) and if the given number is substracted from the denominator, it reduces to (1/3)

You have to find the fraction.

This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.

This is the Question Number 20 Of Exercise 3E of RS Aggarwal Solution

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# If 2 added to the numerator of a fraction, it reduces to (1/2) and if 1 is subtracted from the denominator, it reduces to (1/3). Find the fraction.

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Let the fraction be x/y

Given that

x+2/y =1/2 —–> equ i

x/y-1 =1/3 —–> equ ii

From i and ii

2(x+2) =1(y) ——-> equ i

3(x) =1(y-1) ——-> equ ii

=> 2x+4=y

3x=y-1

Subtract i and ii. we get

2x – y = -4

3x – y = -1

(-) (+) = (+)

______________

-x = -3

_____________

=> x=3

subtitute x=3 in equ i. we get

2(3+2)=y

=> 2(5) =y

=> y=10

Therefore the value of x and y are 3 and 10 respectively.