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Question

A survey shows that in a city, 45% citizens like tea, whereas 65% citizens like coffee. If x% like both tea and coffee, then

A
x=45
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B
x=10
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C
10x45
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D
45x55
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Solution

The correct option is C 10x45
Let the population of the city be 100.
T and C represent the people who like tea and coffee respectively.
n(T)=45, n(C)=65

n(TC)=n(T)+n(C)n(TC)
n(TC)=110n(TC)n(TC)=110n(TC)
We know that,
n(TC)100n(TC)100110n(TC)10n(TC)10 (1)

Now, n(TC)n(T); n(TC)n(C)
n(TC)45; n(TC)65n(TC)45 (2)

From equations (1) and (2),
10x45

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