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All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data ? 1. 40% members went for shopping as well as sightseeing. 2. 20% members went for only shopping. Select the correct answer using the code given below:

All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data ? 1. 40% members went for shopping as well as sightseeing. 2. 20% members went for only shopping. Select the correct answer using the code given below: Correct Answer 1 only

 

n(A U B) = n(A) + n(B) - n(A ꓵ b) 

Let the total no. of people be 100.

People who went for shopping = 80% of 100 = 80 = n(A)

People went for sightseeing = 50% of 100 = 50 = n(B)

People who took rest = 10% of 100 = 10

People who went for shopping or sightseeing or both = 100 - 10 = 90 = n(A U B)

Therefore,

90 = 80 + 50 - n(A ꓵ b) 

n(A ꓵ b) = 130 - 90

n(A ꓵ b)  = 40

People who went for shopping as well as sightseeing = 40

People who went for only shopping = 80 - 40 = 40

People who went for only sightseeing = 50 - 40 = 10

Conclusion 1 : 40% members went for shopping as well as sightseeing. (True)

Conclusion 2 : 20% members went for only shopping. (False)

Hence, option 1 is the correct answer.

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