QUESTION

CSAT

Easy

Reasoning

Prelims 2019

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 a rest in the hotel.

Which of the following conclusion(s) can be drawn from the above data?

$40\%$ of members went for shopping as well as sightseeing.
$20\%$ of members went for only shopping.

Select the correct answer using the code given below:

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Explanation

Step 1: Since 10% took a rest, 90% went for either shopping or sightseeing or both.

Step 2: Use the principle of inclusion-exclusion to find the percentage of members who went for both shopping and sightseeing. $|S \cup T| = |S| + |T| - |S \cap T|$

Substitute the known values: $90 = 80 + 50 - |S \cap T|$

Solve for $|S \cap T|$ : $|S \cap T| = 80 + 50 - 90 = 40$ %

Step 3: The percentage of members who went for only shopping is the total percentage who went for shopping minus those who went for both shopping and sightseeing: Only Shopping = $|S| - |S \cap T| = 80\% - 40\% = 40\%$