Question

If in a group of goats and hens, the number of legs is 24 more than the twice the number of heads, then the number of goats in the group is:
(a) 18
(b) 14
(c) 16
(d) 12

Answer 1

Hint: Start by letting the number of goats be x and number of hens be y. Focus on the point that a goat has 4 legs and 1 head while the hen has a head and 2 legs. So, use this along with the statement given in the question to form the equation and solve it to get the value of x.

Complete step by step solution:
Let us start the solution to the above question by letting the number of goats be x and number of hens be y.
Now we know that a goat has 4 legs and 1 head while the hen has a head and 2 legs. So, the total number of legs is equal to (2y+4x) and the number of heads is equal to (x+y). It is also given in the question that the number of legs is 24 more than the twice the number of heads. So, if we represent this mathematically, we get
$2y+4x=24+2\left( x+y \right)$
Now we will multiply and open the bracket. On doing so, we get
$2y+4x=24+2x+2y$
$\Rightarrow 2y+4x-2x-2y=24$
$\Rightarrow 2x=24$
$\Rightarrow x=12$
Therefore, the total number of goats is 12. Hence, the answer to the above question is option (d).

Note: If we were asked the number of hens in the above question, the answer would have been any number, as there can be any number of hens and there is no constraint on the number of hens. Such questions are generally solvable for very particular cases where one of the variables is cancelled and we are left out with a linear equation in a single variable. Mostly, if a question has two variables you will need to have two equations for solving it.