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Question

In a party, $$70$$ guests were to be served tea or coffee after dinner. There were $$52$$ guests who preferred tea while $$37$$ preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee?


A
15
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B
18
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C
19
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D
33
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Solution

The correct option is C $$19$$
Total number of guests $$= 70$$
Let $$A$$ and $$B$$ be the guests who preferred tea and coffee respectively.
$$n(A)=52$$
$$n(B)=37$$
$$n(A\cup B)=70$$
$$n(A\cup B) = n(A)+n(B)-n(A\cup B)$$
$$=52+37-70=89-70=19$$
Guests who liked both tea and cofffee  $$=19$$


940660_514826_ans_7f7b328629014a05905b12db230d2d8e.png

Mathematics

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