Question

Half a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. If the remaining 9 are drinking water from a pond ,then the difference between the number of deer who are grazing and those who are playing is a multiple of

• A. $4$
• B. $6$
• C. $8$
• D. $9$

Answer 1

The correct option is D $9$

Let $x$ be the total number of deer.

$\frac{x}{2}$ deers are grazing in the field and $\frac{3}{4}$ of $\frac{x}{2}$ are playing.

There are $9$ remaining deer.

$\therefore$ $\frac{3}{4}\times \frac{x}{2}+9=\frac{x}{2}$

$⟹$ $\frac{3x}{8}-\frac{x}{2}=-9$

$⟹$ $\frac{-2x}{16}=-9$

$⟹$ $x=72$

$\therefore$ $36$ deers are grazing in the field and $27$ are playing.

$\therefore$ no. of deers grazing $-$ no. of deers playing $=36-27=9$ which is the multiple of $3$ and $9$.

Hence, option D is correct.