Question

If the ratios $2:a$ and $8:b$ are equivalent, then possible value(s) of $a$ and $b$ is/are

• A. $a=1,b=2$
• B. $a=3,b=12$
• C. $a=4,b=16$
• D. $a=2,b=6$

Answer 1

Answer: (B), (C)

$a=4,b=16$

Given, the ratios $2:a$ and $8:b$ are equivalent.
$\therefore \frac{2}{a}=\frac{8}{b}$
Cross multiplying, we get

$2\times b=a\times 8$
$\Rightarrow \frac{b}{a}=\frac{8}{2}$
$\Rightarrow \frac{b}{a}=4$

Let's check whether each option results in 4 by dividing the values for "b" with the values for "a".

$\left(A\right)a=1,b=2$
Here, $\frac{b}{a}=\frac{2}{1}=2\ne 4$
$\to \text{REJECTED}$

$\left(B\right)a=3,b=12$
Here, $\frac{b}{a}=\frac{12}{3}=4$
$\to \text{ACCEPTED}$

$\left(C\right)a=4,b=16$
Here, $\frac{b}{a}=\frac{16}{4}=4$
$\to \text{ACCEPTED}$

$\left(D\right)a=2,b=6$
Here, $\frac{b}{a}=\frac{6}{2}=3\ne 4$
$\to \text{REJECTED}$