QUESTION

# Half of a herd of deer are grazing in the field and three fourth of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Hint: As, initially, we don’t know about the total number of deer in the herd. Assume it something i.e. take a variable to assume its value equal to the total number of deer in the herd. Then, solve the question accordingly, and eventually, in the end, you will get the value of that variable.

Therefore, the number of deer grazing in the field = $\dfrac{X}{2}$
So, the number of remaining deer = $\dfrac{X}{2}$
Hence, the number of deer playing nearby = $\dfrac{3}{4}\times \dfrac{X}{2}=\dfrac{3X}{8}$ (As, three fourth of the remaining deer are playing nearby.)
$\Rightarrow \dfrac{1}{4}\times \dfrac{X}{2}=\dfrac{X}{8}$
According to the question, $\dfrac{X}{8}=9\Rightarrow X=72$