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Answer :
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.