In a group of 26 persons, 8 take tea but not coffee and 16 take tea. The number of persons who take coffee but not tea is :

The correct answer is (d) 10.

Let $T$ be the set of people who take tea and $C$ be the set of people who take coffee. We are given that $|T|=16$ and $|T\cap C|=8$. We want to find $|C\setminus T|$, the number of people who take coffee but not tea.

We know that $|T\cup C|=26$, so $|C|=|T\cup C|-|T\cap C|=26-8=18$. Therefore, $|C\setminus T|=|C|-|T|=18-16=10$.

Option (a) is incorrect because $24$ is greater than $18$. Option (b) is incorrect because $20$ is greater than $18$. Option (c) is incorrect because $18$ is the total number of people who take coffee, not the number of people who take coffee but not tea.