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Question
A survey shows that 63% of the people watch a News Channel whereas 76% watch another channel. If x% of the people watch both channel, then ______.
Options
x = 35
x = 63
39 ≤ x ≤ 63
x = 39
Solution
A survey shows that 63% of the people watch a News Channel whereas 76% watch another channel. If x% of people watch both channel, then 39 ≤ x ≤ 63.
Explanation:
Let p% of the people watch a channel and q% of the people watch another channel
∴ n(p ∩ q) = x% and n(p ∪ q) ≤ 100
So n(p ∪ q) ≥ n(p) + n(q) – n(p ∩ q)
100 ≥ 63 + 76 – x
100 ≥ 139 – x
⇒ x ≥ 139 – 100
⇒ x ≥ 39
Now n(p) = 63
∴ n(p ∩ q) ≤ n(p)
⇒ x ≤ 63
So 39 ≤ x ≤ 63.
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