Question

$a:2$ and $4:8$ are equivalent ratios. Also, $2:b$ and $6:3$ are equivalent ratios. What is the value of $a+b$ ?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

We can write $4:8$ as $1\times 4:2\times 4=1:2$

$\because$ $a:2$ and $4:8$ are equivalent, their simplest forms are equal.
$\Rightarrow$ Simplest form of $a:2$ is $1:2$.

$\Rightarrow$ $\frac{a}{2}=\frac{1}{2}$

Multiplying both sides with $2$, we get

$\Rightarrow$ $a=1$

Also,
$6:3$ $\Rightarrow$ $2\times 3:1\times 3=2:1$

$\because$ $2:b$ and $6:3$ are equivalent, their simplest forms are equal.
$\Rightarrow$ Simplest form of $2:b$ is $2:1$

$\Rightarrow$ $\frac{2}{b}=\frac{2}{1}$

Multiplying both sides with $b$ , we have

$2b=2$ $\Rightarrow$ $b=1$

$\therefore$ $a+b=1+1=2$