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# The sum of numerator and denominator of a fraction is 8. If 3 is added to both of the numerator and the demoniator, the fraction becomes 3/4. Find the fraction.

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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 19 Exercise 3E of RS Aggarwal Solution
Here The sum of numerator and denominator of a fraction is given. if the given number is added to both of the numerator and the demoniator, the fraction becomes 3/4.
you have to find the fraction.

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1. As the sum of the numerator and the denominator of a fraction is 8, we can take the numerator and denominator as x and 8 – x respectively or vice versa.
Here the numerator and the denominator are taken as x and 8 – x respectively.
x/(8-x)
Given that the fraction becomes 3/4 if 3 is added to both the numerator and the denominator each.
(x+3)/(8-x+3)=3/4
(x+3)/(11-x)=3/4
4(x+3)=3(11-x)
4x+12=33-3x
4x+3x=33-12
7x=21
x=3
Hence the value of x is 3. Thus the numerator is 3.
8-x=8-3=5
Hence the denominator is 5.

Thus, the fraction is 3/5

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