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Question
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.
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`
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