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 :

(a) 1 only ✓ UPSC's answer
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Why the answer is (a)

• Let the total number of members be 100%.

• The percentage of members who went for shopping is 80%, and for sightseeing is 50%.

• The percentage of members who took rest is 10%, meaning 90% of members were active (shopping or sightseeing or both).

• Using the principle of inclusion-exclusion: (Shopping + Sightseeing) - (Both) = Active Members.

• Substituting the values: 80% + 50% - (Both) = 90%, which gives (Both) = 40%.

• Therefore, 40% of members went for both shopping and sightseeing, making statement 1 correct.

Why the other options are wrong

(b) 2 only: Statement 2 is incorrect because the percentage of members who went for only shopping is 40% (80% total shopping minus 40% who did both), not 20%.
(c) Both 1 and 2: This option is incorrect because statement 2 is false, as only 40% went for only shopping, not 20%.
(d) Neither 1 nor 2: This option is incorrect because statement 1 is true, as 40% of members indeed went for both activities.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.