Question

If x: y = 2:7 and y: z = 9:11, find x:y:z.
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Answer 1

Answer:

x:y = 2:7 = 18 : 63

y:z = 9:11 = 63: 77

x:y:z = 18:63:77

Answer 2

To find : $x : y : z$

Given : $x : y = 2: 7 \ and \ y : z = 9 : 11$

Solution :

• To find $x : y : z$  we write in the form of  $\frac{x}{y} \ and \ \frac{y}{z}$
• From ratio $\frac{x}{y} = \frac{2}{7}$ we find value of $x$ .

• substitute the value of $x$ in  $x : y : z$

• Then by cross multiplying we find value of $x : y : z$

                 $\begin{array}{l}\frac{\mathrm{x}}{\mathrm{y}}=\frac{2}{7} \quad \frac{\mathrm{y}}{\mathrm{z}}=\frac{9}{11} \\\mathrm{x}=\frac{2}{7} \mathrm{y} \\\mathrm{x}: \mathrm{y}: \mathrm{z}=\frac{2}{7} \mathrm{y}: \mathrm{y}: \frac{11}{9} \mathrm{y} \\=\frac{2}{7}: 1: \frac{11}{9} \mathrm{y} \\=\frac{2 \times 63}{7}: 63: \times \frac{11}{9} \times 63 \\=18: 63: 77\end{array}$  

Hence value of  $x : y : z$  is $18 : 63 : 77$ .