+1 vote
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There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that $85$% of viewers respond to Bang, $20$% to Luck. and $30$% to Ahead. $20$% of viewers respond to exactly two channels and $5$% to none.

What percentage of the viewers responded to all three?

1. $10$
2. $12$
3. $14$
4. None of these

+1 vote

5(none)

Now,
(1) + (2) + (4) + (5) = 85 (BANG)…..(i)
(2) + (3) + (5) + (6) = 20 (LUCK)…..(ii)
(4) + (5) + (6) + (7) = 30 (AHEAD)…(iii)
(1) + (2) + (3) + (4) + (5) + (6) + (7) = 100 – 5 = 95 …(iv)
(2) + (4) + (6) = 20 ….. (v)
Npw
(i) + (ii) + (iii) – (iv) – (v) gives
2(5) = 135 – 95 – 20 = 20
(5) = 10
Option A is the Correct Answer.