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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 the number of deer = x.
As per the condition given, we have

$$\frac { x }{ 2 }$$ deer are grazing in the field.

Remaining deers=$$x-\frac{x}2=\frac{x}2$$

∴ we have $$\frac{x}2×\frac{3}4=\frac{3x}8$$ deers playing near by.

Number of the deers drinking water=9

∴ we have, $$\frac{x}2+\frac{4x}2+9=x$$

$$\Rightarrow 8×\frac{x}2+8×\frac{3x}8+8×9=8×x$$

$$\Rightarrow 4x+3x+72=8x$$

$$\Rightarrow 7x-8x=-72$$

$$\Rightarrow -x=-72$$

$$\Rightarrow x=72$$

Hence the number of deer in the herd is 72.