10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The sum of the numerator and denominator of a fraction is 8. If the denominator is increased by 1, the fraction becomes \[\frac{1}{2}\]. Algebraic representation of the situation can be:

A) \[x+y=8,\,\,\frac{x+1}{y}=\frac{1}{2}\]

B) \[x+y=8,\,\,\frac{x}{y}+1=\frac{1}{2}\]

C) \[\frac{x}{y}=8,\,\frac{x}{y+1}=\frac{1}{2}\]

D) \[x+y=8,\,\frac{x}{y+1}=\frac{1}{2}\]

Correct Answer: D

Solution :

[d] Let the numerator and denominator of the fraction be x and y respectively.

According to the question,

\[x+y=8\]

and \[\frac{x}{y+1}=\frac{1}{2}\]