Three times a number exceeds its one-third by 64. The number is

1. 24
2. 36
3. 42
4. 48

Let the number be x.

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

According to the question, three times a number exceeds its one-third by 64:

$\therefore 3x - \dfrac{x}{3} = 64 \\[1em] \Rightarrow \dfrac{9x - x}{3} = 64 \\[1em] \Rightarrow 8x = 64 \times 3 \\[1em] \Rightarrow 8x = 192 \\[1em] \Rightarrow x = \dfrac{192}{8} \\[1em] \Rightarrow x = 24$

Hence, option 1 is the correct option.