Q36 / 90 · JEE Main 2021 (26 Aug Shift 1) · Mathematics

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set:

  • Correct answer
    A
    {79,81,83,85}
  • B
    {84,87,90,93}
  • C
    {80,83,86,89}
  • D
    {84,86,88,90}

Solution

Let H and L is set of people suffered from heart ailment and lungs infections respectively.

nH=89%

nL=98%

nH∩L=K%

maxn(H), nL≤nH∪L≤nU

Where, U is the universal set.

⇒98≤nH∪L≤100

⇒98≤nH+nL-nH∩L≤100

⇒98≤89+98-k≤100

⇒0≤89-k≤2

⇒-89≤-k≤-87

⇒87≤K≤89

Hence, the correct answer is option: 'A'.

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