GATE Civil Engineering
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In a company, $35\%$ of the employees drink coffee, $40\%$ of the employees drink tea and $10\%$ of the employees drink both tea and coffee. What $\%$ of employees drink neither tea nor coffee?

  1. $15$
  2. $25$
  3. $35$
  4. $40$
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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  $(C).$
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