Question

Half of a herd of deer are gazing in the field and three fourth of the remaining are playing near by. If the remaining $9$ are drinking water from a pond, then the difference between the number of deer who are gazing 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 the number of deers $=x$
Number of deers grazing $=\frac{x}{2}$
Number of deers playing $=\frac{3}{4}(x-\frac{x}{2})=\frac{3}{8}x$
Number of deers drinking water $=9$
Thus, $\frac{x}{2}+\frac{3x}{8}+9=x$
$\Rightarrow 4x+3x+72=8x$
$\Rightarrow x=72$
Thus, number of deers grazing $=36$
and number of deers drinking playing = $27$
Thus, difference $=36-27=9$
Therefore, it is a multiple of $9$.