Given:
Total number of people = 200
People who prefer coffee = 105
People who prefer tea = 50
The remaining prefer both.
To find:
The fraction of people who prefer both tea and coffee.
Solution:
The number of remaining people who prefer both tea and coffee is
Remaining people = Total number of people - People who prefer coffee - People who prefer tea
Remaining people = 200 - 105 - 50
= 45
Now, the fraction of people who prefer both tea and coffee is
[tex]\text{Required fraction}=\dfrac{\text{Remaining people}}{\text{Total number of people}}[/tex]
[tex]\text{Required fraction}=\dfrac{45}{200}[/tex]
[tex]\text{Required fraction}=\dfrac{9}{40}[/tex]
Therefore, [tex]\dfrac{9}{40}[/tex] of people prefer both tea and coffee.
