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.           

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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 both60=150-Number of students who passes in bothNumber of students who passes in both=150-60=90If we represent passed student in Physics by nA and those in Maths by nBnA=150nB=200nAB=90nAB represents students who passes atleast one subject. nAB=nA+nB-nAB=150+200-90=260Hence students who failed in both=300-260=40 

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