350 people are living in a particular village. There are three drinks tea, coffee and Hot chocolate available in the village. Each citizen has to vote for one or more of the three drinks which he/she like. It is known that 1) In total 120 people like Tea and 160 people like coffee. 2) 46 people like all the three drinks. 3)62 people like both Tea and Hot chocolate. 4) 53 people like both Hot chocolate and Coffee. 5) 89 people lie both Tea and Coffee. 6)How many people like only Tea?Choices:- 15 17 9 29
Question
350 people are living in a particular village. There are three drinks tea, coffee and Hot chocolate available in the village. Each citizen has to vote for one or more of the three drinks which he/she like. It is known that 1) In total 120 people like Tea and 160 people like coffee. 2) 46 people like all the three drinks. 3)62 people like both Tea and Hot chocolate. 4) 53 people like both Hot chocolate and Coffee. 5) 89 people lie both Tea and Coffee. 6)How many people like only Tea?Choices:- 15 17 9 29
Solution
To solve this problem, we need to break down the information given into different categories.
- Total people who like Tea = 120
- Total people who like Coffee = 160
- People who like all three drinks = 46
- People who like both Tea and Hot chocolate = 62
- People who like both Hot chocolate and Coffee = 53
- People who like both Tea and Coffee = 89
First, we need to find out how many people like only Tea.
To do this, we subtract the number of people who like all three drinks and the number of people who like both Tea and another drink from the total number of people who like Tea.
So, people who like only Tea = Total people who like Tea - (People who like all three drinks + People who like both Tea and Hot chocolate + People who like both Tea and Coffee)
However, we have counted the people who like all three drinks twice in the above calculation, so we need to add them back once.
So, people who like only Tea = 120 - (46 + 62 + 89) + 46 = 120 - 197 + 46 = -77 + 46 = -31
Since the number of people cannot be negative, there seems to be a mistake in the problem. The number of people who like both Tea and another drink cannot be more than the total number of people who like Tea. Please check the problem and try again.
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