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Given that, the percentage of employees who drinks coffee $n(C) = 35\%,$ the percentage of employees who drinks tea $n(T) = 40\%,$ and the percentage of employees who drink both tea and coffee $n(C \cap T) = 10\%.$

Total employee $n(U) = 100\%.$

The percentage of employees who drink either tea or coffee $n(C \cup T) = n(C) + n(T) – n(C \cap T)$

$\implies n(C \cup T) = 35 + 40 – 10 = 65\%.$

Now, the percentage of employees who drink neither tea nor coffee $\overline{n(C \cup T)} = n(U) – n(C \cup T)$

$\implies \overline{n(C \cup T)} = 100 – 65 = 35\%.$

So, the correct answer is $(C).$

Total employee $n(U) = 100\%.$

The percentage of employees who drink either tea or coffee $n(C \cup T) = n(C) + n(T) – n(C \cap T)$

$\implies n(C \cup T) = 35 + 40 – 10 = 65\%.$

Now, the percentage of employees who drink neither tea nor coffee $\overline{n(C \cup T)} = n(U) – n(C \cup T)$

$\implies \overline{n(C \cup T)} = 100 – 65 = 35\%.$

So, the correct answer is $(C).$