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 the number of Deer in the herd.​

Answer 1

$\sf\boxed{\underline{\huge{\rm{Solution:}}}}$

$\rm{Let\: the \:number \:of\:deer \:=\: x}$

∴ $\rm{Deer\: grazing\:in\:the\: field=\dfrac{x}{2}}$

$\rm{Remaining\:deer\:=x-\dfrac{x}{2}=\dfrac{x}{2}}$

$\rm{Deer\:playing\:nearby\:=\dfrac{3}{4}×\dfrac{x}{2}=\dfrac{3x}{8}}$

$\rm\underline{According\:to\:the\: question,}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:x-\dfrac{x}{2}-{3x}{8}=9$

$\implies\dfrac{8x-4x-3x}{8}=9$

$\implies\dfrac{x}{8}=9$

$\implies\red{x=72}$

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Answer 2

There are 72 deers in the herd.

Step-by-step explanation:

Half of a herd of deers are grazing.

Three fourths of the remaining are playing nearby.

(Three fourths of the remaining means three fourths of the other half)

Rest 9 are drinking water.

Total deers in the herd = ??

Consider, the total number of deers as y.

Number of deers grazing = Half of the herd

$\sf{\longrightarrow} \: \dfrac{1}{2}y$

Number of deers playing = Three fourths of the remaining

Half are grazing, which means half are remaining.

$\sf{\longrightarrow} \: \dfrac{1}{2}y \times \dfrac{3}{4}$

$\sf{\longrightarrow} \: \dfrac{3}{8}y$

★ Total deers in herd = Deers grazing + Deers playing + 9 deers drinking water

$\sf{\longrightarrow} \: y = \dfrac{1}{2} y + \dfrac{3}{8}y + 9$

$\sf{\longrightarrow} \: y = \dfrac{4y + 3y}{8} + 9$

$\sf{\longrightarrow} \: y = \dfrac{7}{8}y + 9$

$\sf{\longrightarrow} \: y - \dfrac{7}{8}y = 9$

$\sf{\longrightarrow} \: \dfrac{8y - 7y}{8} = 9$

$\sf{\longrightarrow} \: \dfrac{y}{8} = 9$

$\sf{\longrightarrow} \: y = 9 \times 8$

$\sf{\longrightarrow} \: y = 72$

Total number of deers in the herd = 72

Therefore, there are 72 deers in the herd.