Haryana Police Constable Model Paper 1

Difference and sum of x and y are in ratio 1 ∶ 7,
$\Rightarrow \frac{\left(\mathrm{x}-\mathrm{y}\right)}{\left(\mathrm{x}+\mathrm{y}\right)}=\frac{1}{7}$
$\Rightarrow 7\mathrm{x}-7\mathrm{y}=\mathrm{x}+\mathrm{y}$
$\Rightarrow 6\mathrm{x}=8\mathrm{y}$
$\Rightarrow \mathrm{y}=\frac{3\mathrm{x}}{4}$ ....(1)
Also,
Difference and sum of y and z are in ratio 1 ∶ 3,
$\Rightarrow \frac{\left(\mathrm{y}-\mathrm{z}\right)}{\left(\mathrm{y}+\mathrm{z}\right)}=\frac{1}{3}$
$\Rightarrow 3\mathrm{y}-3\mathrm{z}=\mathrm{y}+\mathrm{z}$
$\Rightarrow 2\mathrm{y}=4\mathrm{z}$
$\Rightarrow \mathrm{y}=2\mathrm{z}$
Substituting from (1),
$\Rightarrow \frac{3\mathrm{x}}{4}=2\mathrm{z}$
$\Rightarrow \frac{\mathrm{x}}{\mathrm{z}}=\frac{8}{3}$
∴ Required ratio = x ∶ z = 8 ∶ 3