Question:
In a survey of 250 people about three activities (Reading, Sports, Travel), the following data are given:
130 like Reading,
110 like Sports,
120 like Travel,
55 like both Reading and Sports,
50 like both Sports and Travel,
45 like both Reading and Travel,
25 like all three.
How many like only Travel?
In a survey of 250 people about three activities (Reading, Sports, Travel), the following data are given:
130 like Reading,
110 like Sports,
120 like Travel,
55 like both Reading and Sports,
50 like both Sports and Travel,
45 like both Reading and Travel,
25 like all three.
How many like only Travel?
130 like Reading,
110 like Sports,
120 like Travel,
55 like both Reading and Sports,
50 like both Sports and Travel,
45 like both Reading and Travel,
25 like all three.
How many like only Travel?
Show Hint
For “only” in three-set Venn problems, always subtract the two-way intersections and add back the three-way intersection.
Updated On: Dec 4, 2025
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The Correct Option is D
Solution and Explanation
To find the number of people who like only Travel, compute:
\[
\text{Only Travel} = T - (T \cap R) - (T \cap S) + (R \cap S \cap T).
\]
Given:
$T = 120$,
$T \cap R = 45$,
$T \cap S = 50$,
$R \cap S \cap T = 25$.
Substitute:
\[ \text{Only Travel} = 120 - 45 - 50 + 25 = 50. \] Final Answer: 50
$T = 120$,
$T \cap R = 45$,
$T \cap S = 50$,
$R \cap S \cap T = 25$.
Substitute:
\[ \text{Only Travel} = 120 - 45 - 50 + 25 = 50. \] Final Answer: 50
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