Question

$x:2a46b$

$y:1025c3045$

$z:90def20$ $x,y,z$ are proportional to each other. Which of the following is correct

• A. $a+b=15$
• B. $e+f=65$
• C. $d-b=27$
• D. $c+e=75$

Answer 1

The correct option is C $d-b=27$

$\frac{x}{y}=\frac{2}{10}=\frac{6}{30}=\frac{1}{5}=constant\Rightarrow x\propto y$

$y\times z=10\times 90=45\times 20=900=constant\Rightarrow y\propto \frac{1}{z}$

$x\propto y$ and $y\propto \frac{1}{z}\Rightarrow x\propto \frac{1}{z}$

$\frac{2}{10}=\frac{a}{25}=\frac{4}{c}=\frac{6}{30}=\frac{b}{45}=\frac{1}{5}$

$\Rightarrow a=\frac{25}{5},c=4\times 5=20,b=\frac{45}{5}=9$
$2\times 90=4\times 4=6\times f=b\times 20=180$

$\Rightarrow e=45,f=\frac{180}{6}=30,b=\frac{180}{20}=9$
$10\times 90=25\times d=900$
$\Rightarrow d=\frac{900}{25}=36$

$\Rightarrow d-b=36-9=27$