In a survey conducted among 120 people, the responses of 80% were recorded as the given Venn diagram. If 50 people preferred coffee over tea and 35 people preferred tea over coffee, how many people liked both coffee and tea?

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Solution

The correct option is C 11
$N u m b e r o f r e s p o n s e s r e c o r d e d a s p e r t h e V e n n d i a g r a m$

$= 80 % o f 120 = \frac{80}{100} \times 120 = 96$

$P e o p l e w h o p r e f e r c o f f e e o v e r t e a = 50$

$P e o p l e w h o p r e f e r t e a o v e r c o f f e e = 35$

$T o t a l n u m b e r o f p e o p l e w h o p r e f e r o n e b e v e r a g e o v e r t h e o t h e r$

$= 50 + 35 = 85$

$N u m b e r o f p e o p l e w h o l i k e b o t h t e a a n d$

$c o f f e e = 96 - 85 = 11$

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