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# The denominator of a fraction is greater than its numerator by 11. if 8 is added to both its numerator and denominator, it becomes 3/4. Find the fraction.

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ICSE & CBSE Board Question Based on Linear Equations in two Variables of RS Aggarwal
Here the denominator of a fraction is greater than its numerator by the given number. if a number is added to both its numerator and denominator, it becomes 3/4.
You have to find the fraction.
This is the Question Number 21 Of Exercise 3E of RS Aggarwal Solution.

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1. Let the required fraction be x/y .
According to the Question
1st Equation
â‡’ y = x + 11
â‡’ y â€“ x = 11 â€¦â€¦(i)
2nd Equation
â‡’ x+8/y+8 = 3/4
â‡’ 4(x + 8) = 3(y + 8)
â‡’ 4x+ 32 = 3y + 24
â‡’ 4x â€“ 3y = -8 â€¦â€¦(ii)
On multiplying Equation(i) by 4
4y â€“ 4x = 44
On adding Eq (ii) and (iii)
â‡’ y = (-8 + 44)
â‡’ y = 36
on substituting y = 36 in (i), we get:
â‡’ y â€“ x = 11
â‡’ 36 â€“ x = 11
â‡’ x = (36 â€“ 11)
â‡’ x = 25
Hence, the required fraction is 25/36

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