Question

100 employees in on office were asked about, their preference for tea and coffee. It was observed that for every 3 people who preferred tea, there were 2 people who preferred coffee and there was a person who preferred both the drinks. The number of people who drink neither of them is same as those who drink both. (1) How many people preferred both the drinks? (2) How many people preferred only me drink? (3)How many people preferred at most one drink?​

Answer 1

1. 14
2. 72
3. 86

Explanation:

Given 100 people divided themselves into the ratios ...

prefer tea : prefer coffee : prefer both : prefer neither = 3 : 2 : 1 : 1

You want to know (1) how many prefer both, (2) how many prefer only one drink, (3) how many prefer at most one.

People

Multiplying the given ratio by 100/7, and rounding the results, we have ...

tea : coffee : both : none = 43 : 29 : 14 : 14

(1) Both

Looking at the above ratio, we see ...

14 people preferred both the drinks.

(2) Only one

The number preferring only one is the sum of those preferring tea only and those preferring coffee only:

43 +29 = 72

72 people preferred only one drink.

(3) At most one

This is the number preferring one or none, so will be the above number added to the number who prefer none:

72 +14 = 86

86 people preferred at most one drink.

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Additional comment

The number preferring at most 1 can also be computed as the complement of the number who preferred both: 100 -14 = 86.

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