All 120 students in a class play cricket or football or both, 75 play cricket and 60 play football. How many students play both?
A
13
B
15
C
20
D
25
Correct Answer: 15
<math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo>)</mo><mo> </mo><mo> = </mo><mo> </mo><mi>n</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo> + </mo><mi>n</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo> - </mo><mi>n</mi><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo></math>⇒ 120 = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo> + </mo><mn>60</mn><mo> - </mo><mi>n</mi><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo></math>⸫ <math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo><mo> </mo><mo> = </mo><mo> </mo><mn>15</mn></math>