Question

Divide $150$ into three parts such that the second part is five such that first and the third part is four-fifth the second

Answer 1

Let the 1st number be x.

then, 2nd number will be $\frac{5}{6}x$

3rd number will be $\frac{4}{5}\left(\frac{5}{6}x\right)=\frac{2}{3}x$

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

$\Rightarrow \frac{6x+5x+4x}{6}=150$

$\Rightarrow 15x=150\times 6$

$\Rightarrow x=\left[\frac{150\times 6}{15}\right]=60$

1st number $=60$

2nd number $=\frac{5}{6}x=\frac{5}{6}\times 60=50$

3rd number $=\frac{2}{3}x=\frac{2}{3}\times 60=40$