Question

What term should be added to antecedent and subtracted from consequent of ratio $4:7$ to make a compound ratio of $2:3$ and $5:4$ ? $\left[2\text{Marks}\right]$

Answer 1

Let the number be $x$.

As per question, $(4+x):(7-x)=2\times 5:3\times 4$.
$[\because$ the compound ratio of the ratios $2:3$ and $5:4=2\times 5:3\times 4$ ] $\left[1\text{Mark}\right]$

$\Rightarrow$ $\frac{4+x}{7-x}=\frac{2\times 5}{3\times 4}$
$\Rightarrow$ $\frac{4+x}{7-x}=\frac{5}{6}$
$\Rightarrow$ $24+6x=35-5x$.
$\Rightarrow$ $\dot{6}x+5x=35-24$ or, $11x=11$
$\Rightarrow$ $x=\frac{11}{11}=1$

Hence, the required number $=1$. $\left[1\text{Mark}\right]$