Ratio and Proportion

Concept:Let the unknown number be $x$.Its successor is $x+1$.The problem compares $\frac{1}{3}$ of $x$ with $\frac{1}{4}$ of $(x+1)$ and states the difference is 1.Explanation:One-third of the number: $\frac{x}{3}$.One-fourth of the successor: $\frac{x+1}{4}$.The given condition: $\frac{x}{3}$ is greater than $\frac{x+1}{4}$ by 1.That means: $\frac{x}{3} = \frac{x+1}{4} + 1$.Multiply through by 12 (LCM of 3 and 4) to clear denominators: $12 \cdot \frac{x}{3} = 12 \cdot \frac{x+1}{4} + 12 \cdot 1$.This simplifies to $4x = 3(x+1) + 12$.Expand the right-hand side: $4x = 3x + 3 + 12$.Combine constants: $4x = 3x + 15$.Subtract $3x$ from both sides: $4x - 3x = 15$, so $x = 15$.Thus the required number is 15.Answer:The number is 15.