Question: In the village called TALAJA, only three TV channels are available - Moon Plus, Mony and Mee TV.
Out of 4000 TV viewers in the village, 1500 watch Moon TV, 2000 watch Mony and 2500 watch Mee TV.
Amongst these, 500 viewers watch Moon Plus and Mony, 800 watch Moon Plus and Mee TV, and 1000 watch Mony and Mee TV.
How many viewers watch all three channels?
Answer:
300 viewers watch all three channels.
Let's assume that total X viewers watch all three channels.
total viewers who watch only Moon Plus and Mony = 500-X
total viewers who watch only Moon Plus and Mee TV = 800-X
total viewers who watch only Mony and Mee TV = 1000-X
total viewers who watch only Moon Plus
= 1500 - (500-X) - (800-X) - X
= 200 + X
total viewers who watch only Mony
= 2000 - (500-X) - (1000-X) - X
= 500 + X
total viewers who watch only Mee TV
= 2500 - (1000-X) - (800-X) - X
= 700 + X
We know that total viewers are 4000. Summing up all 7 values,
X + (500 - X) + (800 - X) + (1000 - X) + (200 + X) + (500 + X) + (700 + X) = 4000
X + 3700 = 4000
X = 300
Hence, total 300 viewers watch all three channels.