Question

A man has a certain number of chickens and goats. Their head count is 30. If the total number of their legs is 84, what is the ratio between the number of chickens and goats?

• A. 1 : 2
• B. 2 : 3
• C. 3 : 2
• D. 3 : 4

Answer 1

The correct option is C

3 : 2

Let x and y be the number of chickens & goats respectively

Their headcount is 30.

so, x + y = 30 ....(i)
The total number of their legs is 84. A chicken has two legs whereas a goat has four legs.
So, 2x + 4y = 84 .... (ii)

Multiplying equation (i) by 2, we get

2x + 2y = 60 ....(iii)

Subtracting equation (iii) from (ii), we obtain

2y = 24

y = 12

Plugging this value of y in equation (i)

x + 12 = 30

x = 18

So, we get x=18, y=12

$\therefore$ the ratio between the number of chickens & goats

$\Rightarrow$ $\frac{x}{y}$ = $\frac{18}{12}$ = $\frac{3}{2}$ =3$:$2