Three-fourths of a number exceeds its one-third by 15. Find the number.

Let the required number be x.

Three-fourths of the number = $\dfrac{3}{4}x$

One-third of the number = $\dfrac{1}{3}x$

According to the question, the difference between them is 15.

$\therefore \dfrac{3}{4}x - \dfrac{1}{3}x = 15 \\[1em] \Rightarrow \dfrac{9x - 4x}{12} = 15 \\[1em] \Rightarrow \dfrac{5x}{12} = 15 \\[1em] \Rightarrow 5x = 15 \times 12 \\[1em] \Rightarrow 5x = 180 \\[1em] \Rightarrow x = \dfrac{180}{5} \\[1em] \Rightarrow x = 36$

Hence, the required number is 36.