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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the pop lation like tea and 72% of the population like coffee. Let $x$ be the number of people who like both tea & coffee. Let $m{\leq x\leq n}$, then choose the correct option.
Solution
Total people = 200
People who like tea = \(60\% \times 200 = 120\)
People who like coffee = \(72\% \times 200 = 144\)
People who like tea = \(60\% \times 200 = 120\)
People who like coffee = \(72\% \times 200 = 144\)
Using the set formula: \[ |T \cup C| = |T| + |C| - |T \cap C| \] \[ 200 = 120 + 144 - x \quad \Rightarrow \quad x = 64 \]
Minimum possible intersection: \[ x \geq |T| + |C| - 200 = 64 \] Maximum possible intersection: \[ x \leq \min(120,144) = 120 \]
✅ Final Answer
The range of \(x\) is: 64 ≤ x ≤ 120 Hence, \(m = 64, \; n = 120\).
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i think (1) should be correct because
n(AUB) = 200 , n(A) = 120 , n(B) = 144 , n( A intersection B ) = x
n(AUB) = n(A) + n(B) - n(A intersection B)
x = 120 + 144 -200
x = 64
n = 120 because maximum no. of population like tea is 120
m = 64 as calculated above
so n-m => 120 -64 => 56
hence (1) is correct
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Commented Sep 15 , 2025
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