In a group of 40 people, 25 people speak Hindi and 20 people speak both Hindi…
2025
In a group of 40 people, 25 people speak Hindi and 20 people speak both Hindi and Urdu. All the people speak at least one of the two languages. How many people speak Urdu?
- A.
65
- B.
15
- C.
45
- D.
35
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Let H be the set of Hindi speakers and U be the set of Urdu speakers. We are given that the total number of people n(H ∪ U) = 40, Hindi speakers n(H) = 25, and those who speak both n(H ∩ U) = 20. Using the inclusion-exclusion principle: n(H ∪ U) = n(H) + n(U) - n(H ∩ U). Substituting the known values: 40 = 25 + n(U) - 20. Simplifying the equation: 40 = 5 + n(U). Solving for n(U): n(U) = 35. Thus, 35 people speak Urdu.