Question

Two fractions are given such that their numerators are consecutive integers and their respective denominators are also consecutive integers. If the difference between the fractions is 1 and the difference between the numerator and denominator of each fraction is 2, find the smaller fraction (consider both the fractions to be positive).

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C

2

$\text{Let one fraction be}\frac{x}{y}\text{Then the other fraction is}\frac{x+1}{y+1}x=y+2\frac{x}{y}-\frac{x+1}{y+1}=1\text{Solving the above we get y =1}\frac{x}{y}=3\frac{x+1}{y+1}=2$