Question

Question 4 (ii)
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Answer 1

Let the fraction be $\frac{x}{y}$
According to the question,
$\frac{x-1}{y}=\frac{1}{3}$
$\Rightarrow 3x-y=\mathrm{3....}\left(i\right)$
$\frac{x}{y+8}=\frac{1}{4}$
$\Rightarrow 4x-y=\mathrm{8...}\left(ii\right)$
Subtracting equation (i) from equation (ii), we get
x = 5 ... (iii)
Putting this value in equation (i), we get
15 - y = 3
$\Rightarrow$ y = 12
Hence, the fraction is $\frac{5}{12}$.