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 ratios, their simplest forms are equal.
$\Rightarrow$ Simplest form of 4 : 8 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 ratios, their simplest forms are equal.
$\Rightarrow$ Simplest form of 6 : 3 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