Question

1/x:1/y:/z=2:3:5 then x:y:z

Answer 1

$\displaystyle \frac{1}{x}:\frac{1}{y}:\frac{1}{z} \ = \ 2:3:5 \\ \\ \\ \\ \textit{Consider \ \frac{1}{x}:\frac{1}{y} \ = 2:3 . } \\ \\ \\ \frac{1}{x}:\frac{1}{y} \ = 2:3 \\ \\ \\ \frac{1}{x} \times xy:\frac{1}{y} \times xy \ = 2:3 \\ \\ \\ y:x=2:3 \\ \\ \\ x:y=3:2\ \ \ \ \ \longrightarrow\ \ \ (1)$

$\displaystyle \textit{Consider \ \frac{1}{y}:\frac{1}{z} \ = \ 3:5 .} \\ \\ \\ \frac{1}{y}:\frac{1}{z} \ = \ 3:5 \\ \\ \\ \frac{1}{y} \times yz:\frac{1}{z} \times yz \ = \ 3:5 \\ \\ \\ z:y=3:5 \\ \\ \\ y:z=5:3\ \ \ \ \ \longrightarrow\ \ \ (2)$

$\textit{From (1) ,} \\ \\ \\ x:y=3 \times 5:2 \times 5 \\ \\ \\ x:y=15:10\ \ \ \ \ \longrightarrow\ \ \ (3)$

$\textit{From (2) ,} \\ \\ \\ y:z=5 \times 2:3 \times 2 \\ \\ \\ y:z=10:6\ \ \ \ \ \longrightarrow\ \ \ (4)$

$\textit{From (3) and (4) ,} \\ \\ \\ x:y:z \ = \ \mathbf{15:10:6}$

Answer 2

Answer:

x: y: z  =15:10: 6

Step-by-step explanation:

1/x:1/y:/z=2:3:5

x: y: z = 1/2 :1/3: 1/5 =15/30: 10/30 :6/30 =15:10: 6