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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:

A fraction becomes `1/3` when 1 is subtracted from the numerator and it becomes `1/4` when 8 is added to its denominator. Find the fraction.

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#### Solution

Let the fraction be `x/y`

According to the question,

`(x-1)/y = 1/3`

⇒ 3x - y = 3... (i)

`x/(y+8) = 1/4`

⇒ 4x - y = 8 ... (ii)

Subtracting equation (i) from equation (ii), we get

x = 5 ... (iii)

Putting this value in equation (i), we get

15 - y = 3

y = 12

Hence, the fraction is `5/12`

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

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