let the number 'x'

According to the question

$$\begin{gathered} = \frac{1}{4}x+5=\frac{1}{3}x-5 \\ = \frac{x}{4}+5=\frac{x-3\times 5}{3} \\ =\frac{x}{4}+5=\frac{x-15}{3} [multiply both sides by 12] \\ = 12\times \frac{x}{4}+12\times 5=12\times \frac{x-15}{3} \\ =3x+60=4(x-15) \\ =3x+60=4x-60 \\ =x=120 \end{gathered}$$

Hence, Option D is correct.