A class took two tests, one in physics and other in maths 1/3rd class failed in maths and 1/2th - Maths - Sets

Question

A class took two tests, one in physics and other in maths 1/3rd
class failed in maths and 1/2th class failed in physics 60% of
those who passed in physics also passed in maths if 300 students
took both the test then how many student failed in both

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Total 300 students appeared in the test
Number of students who failed in Physics=12×300=150HenceNumber of students who passes in Physics=300-150=150Number of students who failed in Maths=13×300=100HenceNumber of students who passes in Maths=300-100=20060% of those who passes in Physics=60100×150=90Hence 150-90=60 students who passes in Phyics but failedin MathsNumbe of students who passed in Physics only=Number of students who passes in Physics-Number of students who passes in both⇒60=150-Number of students who passes in both⇒Number of students who passes in both=150-60=90If we represent passed student in Physics by nA and those in Maths by nBnA=150nB=200nA∩B=90nA∪B represents students who passes atleast one subject
 nA∪B=nA+nB-nA∩B=150+200-90=260Hence students who failed in both=300-260=40

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A class took two tests, one in physics and other in maths. 1/3rd class failed in maths and 1/2th class failed in physics. 60% of those who passed in physics also passed in maths. if 300 students took both the test then how many student failed in both.