Divide 150 into three parts such that the second number is five-sixths

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

Then, the second number will be $\frac{5}{6} x$.

Third numbe $r=\frac{4}{5}\left(\frac{5}{6} x\right)=\frac{2}{3} x$

$\therefore x+\frac{5 x}{6}+\frac{2 x}{3}=150$

$\Rightarrow \frac{6 x+5 x+4 x}{6}=150 \quad$ (multiplying the L.H.S. by 6, which is the L.C.M. of 1,6 and 3$)$

$\Rightarrow 15 x=150 \times 6 \quad$ (by cross multiplication)

$\Rightarrow 15 x=900$

$\Rightarrow x=\frac{900}{15}=60$

Therefore, the first number is 60 .

Second number $=\frac{5}{6} x=\frac{5}{6}(60)=50$

Third number $=\frac{2}{3} x=\frac{2}{3}(60)=40$