Out of 52 students , 35 can speak Hindi , 32 can speak English , 31 can speak…
2024
Out of 52 students , 35 can speak Hindi , 32 can speak English , 31 can speak German , 20 speak both Hindi and English , 18 speak both Hindi and German and 24 both English and German . How many can speak all languages ?
- A.
24
- B.
12
- C.
18
- D.
16
Attempted by 30 students.
Show answer & explanation
Correct answer: D
Use the inclusion–exclusion principle:
Total = Hindi + English + German − (Hindi∩English) − (Hindi∩German) − (English∩German) + (Hindi∩English∩German)
Substitute the given numbers:
52 = 35 + 32 + 31 − (20 + 18 + 24) + x
Compute the sums: 35 + 32 + 31 = 98 and 20 + 18 + 24 = 62, so 52 = 98 − 62 + x = 36 + x
Solve for x: x = 52 − 36 = 16
Answer: 16 students speak all three languages.