Four-fifths of a number is 10 more than two-thirds of the number.

Let the number be $\mathrm{x}$.

Four fifths of the number is 10 more than two thirds of the number.

$\therefore \frac{4}{5} x=10+\frac{2}{3} x$

$\Rightarrow \frac{4 x}{5}=10+\frac{2 x}{3}$

$\Rightarrow \frac{4 x}{5}=\frac{30+2 x}{3}$$\quad(L \cdot C \cdot M .$ of 1 and 3 is 3$)$

$\Rightarrow 3(4 x)=5(30+2 x) \quad$ (by cross multiplication)

$\Rightarrow 12 x=150+10 x$

$\Rightarrow 12 x-10 x=150$

$\Rightarrow 2 x=150$

$\Rightarrow x=\frac{150}{2}=75$

Therefore, the number is 75 .