Question:
Four-fifths of a number is 10 more than two-thirds of the number. Find the number.
Solution:
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 .
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