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Most Important Selected Qs for JEE AdvancedMathematicsSets and Relations

A survey shows that 69 % students like mathematics, whereas 75 % like chemistry. If x % students like both the subjects, then the maximum value of x is

Correct answer

69

Step-by-step solution

Let, total students in survey be 100 If mathematics is represented by m & chemistry by c , then n m ∩ c = x Given, n m = 69 ,   n c = 75 Now, n m ∪ c = n m + n c - n m ∩ c = 69 + 75 – x = 144 – x ∵ 75 ≤ n m ∪ c ≤ 100 75 ≤ 144 - x   ≤ 100 ∴ 44 ≤ x ≤ 69

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