# Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby.

**Question:**

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 thenumber of deer in the herd.

**Solution:**

Let the number of deer in the herd be $\mathrm{x}$.

The number of deer grazing in the field is $\left(\frac{1}{2}\right) \mathrm{x}$.

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

$N$ umber of deer playing nearby $=\frac{3}{4}\left(\frac{x}{2}\right)=\frac{3}{8} x$

The number of deer drinking water from the pond is 9 .

$\therefore 9+\frac{3}{8} x+\frac{1}{2} x=x$

$\Rightarrow \frac{72+3 x+4 x}{8}=x \quad($ multiplying the L.H.S. by 8, which is the L.C.M. of 1,8 and 2$)$

$\Rightarrow 72+7 x=8 x \quad$ (by cross multiplication)

$\Rightarrow 72=8 x-7 x$

$\Rightarrow 72=x$

$\Rightarrow x=72$

Total number of deer in the herd $=72$