All members of a club went to Mumbai and stayed in a hotel

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:

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Answer

Members who took rest = 10%

Members who went for either shopping or sightseeing or both = 90%

n(Shopping) = n(A) = 80%

n(Sightseeing) = n(B) = 50%

n(A ∪ B) = 90%

n(A ∩ B) = 80% + 50% - 90% = 40%

So, statement 1 is correct.

Members who went for only shopping = n(A) - n(A ∩ B)

= 80% - 40% = 40%

So, statement 2 is incorrect.

The correct option is A.