Question & Answer
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.

ANSWER Verified Verified
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.

Complete step-by-step answer:
According to the question, half of the total number of deer in the herd is grazing in the field and three fourth of the remaining are playing nearby. It means that the three fourth of the remaining half of the herd are playing nearby.
But, the only data which is given in the figures is that the rest 9 of them are drinking water from the pond. And, we have to find the total number of deer in the herd.
So, to solve the given problem, we have to assume that let the total number of the deer in the herd be X.
As half of the herd of deer are grazing in the field:
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.)
As the rest 9 is drinking water from the pond, it is the one-fourth of the half of the herd of deer.
$\Rightarrow \dfrac{1}{4}\times \dfrac{X}{2}=\dfrac{X}{8}$
According to the question, $\dfrac{X}{8}=9\Rightarrow X=72$
Hence, the number of deer in the herd is 72.

Note: Instead of looking at the calculations, one should always look upon the logic involved in these types of questions. This will also reduce our time and the large calculations involved.