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A survey shows that 63% Indians like coffee while 82% like tea. If x% of the Indians like both coffee and tea, then find the value of ‘x’.
Question

A survey shows that 63% Indians like coffee while 82% like tea. If x% of the Indians like both coffee and tea, then find the value of ‘x’.

A.

x = 18

B.

x = 63

C.

x = 45

D.

None of these

Correct option is C

Given:
Coffee (C) = 63%
Tea (T) = 82%
Intersection (C and T) = x%
Formula Used:
n(CT)=n(C)+n(T)n(CT)100%n(C \cup T) = n(C) + n(T) - n(C \cap T) \le 100\%​​
Solution:
The maximum possible value for the union of both sets is 100%.
10063+82x100 \ge 63 + 82 - x​​
100145x100 \ge 145 - x​​
x45x \ge 45​​
Thus, the minimum percentage of people who like both is 45%. Based on the options provided, x = 45 represents the required mathematical boundary.
Final Answer
So the correct answer is (c)

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