Question

What must be subtracted from each term of the ratio 4:7, so that the ratio becomes 2:9?

• A. $\frac{22}{7}$
• B. $\frac{44}{7}$
  
• C. $\frac{50}{7}$
• D. $\frac{30}{7}$

Answer 1

The correct option is A $\frac{22}{7}$

Consider the term to be subtracted form 4 and 7 as $x$.

$\frac{4-x}{7-x}=\frac{2}{9}$
$\Rightarrow 9(4-x)=2(7-x)$
$\Rightarrow 36–9x=14–2x$
$\Rightarrow 22=7x$
$\Rightarrow$ $x=\frac{22}{7}$

Hence, $\frac{22}{7}$ must be subtracted from each term of the ratio to get 2:9.