Question: In a survey on the viewership of the TV channels, 73% of those surveyed viewed at least one of the three Channels: Star Plus, Sab TV, and Sony. 38% of those surveyed viewed Star Plus, 39% viewed Sony, and 23% viewed Sab TV. 11% of all those surveyed viewed all the three channels. What percentage of those surveyed, viewed more than one of the three TV channels?
Explanation:
Let there be 100 people surveyed in all.
Let a, b, c correspond to people who watched only Star Plus, only Sony and only SAB TV.
Let d, e, f correspond to people who watched only Star Plus and Sony, only Sony and SAB TV and only SAB TV and Star Plus.
Let g correspond to people who watched all three channels.
73% people i.e. 73 people watched atleast one channel.
∴ a + b + c + d + e + f + g = 73 … (i)
Number of people watching Star Plus, Sony and SAB TV is 38%, 39% and 23% respectively i.e. 38, 39 and 23.
∴ a + d + f + g = 38 … (ii)
b + d + e + g = 39 … (iii)
c + e + f + g = 23 … (iv)
Adding (i), (ii) and (iii):
(a + b + c) + 2(d + e + f) + 3g = 39 + 38 + 23 = 100 … (v)
Solving (i) and (v), we get:
(d + e + f) + 2g = 100 – 73 = 27
Number of people surveyed who watch more than one channel = (d + e + f) + g
Also, number of people who watch all channels = g = 11
∴ (d + e + f) + g + 11 = 27
∴ (d + e + f) + g = 16
∴ Required % = (16/100) × 100 = 16%
Hence, option (a).