# Q.8 Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Let us assume the number of deer in the herd to be x.

Half of a herd of deer are grazing in the field i.e.,   $\frac{x}{2}$.

Now half are remaining.

Three fourths of the remaining are playing nearby, implies :

$\frac{3}{4}\times \frac{x}{2} = \frac{3x}{8}$

Remaining number of deer will be :

$\frac{x}{2} - \frac{3x}{8} = \frac{4x - 3x}{8} = \frac{x}{8}$

Given that rest are 9, so

$\frac{x}{8} = 9$

Hence number  of deer in the herd = 72

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