Question

In a survey conducted on 200 people, it was found that 105 of them prefer coffee, 50 prefer

tea and the remaining prefer both. Find the fraction of people who prefer both tea and coffee.

Answer 1

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

`\text{Required fraction}=\frac{\text{Remaining people}}{\text{Total number of people}}`

`\text{Required fraction}=(45)/(200)`

`\text{Required fraction}=(9)/(40)`

Therefore,
`(9)/(40)` of people prefer both tea and coffee.