Question

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
(i) The sum of the numerator and denominator of a fraction is 24. If we subtract 4 from the numerator and 5 from its denominator, then it reduces to $\frac{1}{4}$. Determine the given fraction.

Answer 1

Dear Student,


$$\begin{gathered} letthefractionis\frac{a}{b} \\ giventhata+b=24\to 1 \\ \frac{a-4}{b-5}=\frac{1}{4} \\ 4a-16=b-5 \\ 4a-b=11\to 2 \\ from1\&2 \\ a+b=24 \\ 4a-b=11 \\ \overline{5a=35} \\ a=7 \\ b=24-7 \\ b=17 \\ \therefore \frac{a}{b}=\frac{7}{17} \end{gathered}$$

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