Q. 383.8( 9 Votes )
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
A. x = 35
B. x = 63
C. 39 ≤ x ≤ 63
D. x = 39
Answer :
Given: 63% of the people watch a News Channel whereas 76% watch another channel
To find: x% of the people watch both channel, then value of x
Let p% and q% of people watch a news channel and another channel respectively
n(p)= 63, n(q) = 76, n(p ∩ q) = x, n(p ∪ q) 
100
We know,
n(p ∪ q) 
n(p) + n(q) – n(p ∩ q)
⇒ 100 
63 + 76 – x
⇒ x 
139 – 100
⇒ x 
39
Now,
n(p ∪ q) 
n(p) and n(p ∪ q) 
n(q)
⇒ x 
63 and x 
76
Hence, 39 
x 
63
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