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600 students took the test on Physics and chemistry. 35% students failed in Physics and 45% students failed in chemistry and 40% of those who passed in chemistry also passed in Physics, then how many students failed in both :

A. 16

B. 15

C. 13

D. 12

Answer: Option D

Solution(By Examveda Team)

Result PhysicsChemistry
Failed35%45%
Passed65%55%


Now, 55% of 600 passed in Chemistry = $$\frac{{55 \times 600}}{{100}}$$   = 330
From question, 40% of those who passed in Chemistry(330 Students) also passed in physics
= $$\frac{{40 \times 330}}{{100}}$$
= 132,
so, 132 students passed in both
Therefore % who passed in both = $$\frac{{132 \times 100}}{{600}} = 22\% $$
Passed in both subject = 22% of total students
% of students who passed in either Physics or Chemistry or both,
= (65 + 55) - 22
= 98%
Thus, percentage of students who failed in both subjects = 2%
Number of students who failed = 2% of 600 = 12

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Comments ( 5 )

  1. Ashraful Islam
    Ashraful Islam :
    4 years ago

    Physics failed = 35%,Pass = 65%
    Chemistry failed = 45%, Pass = 55%, Both Pass = 40% of 55% = 22%
    Total failed = 78%
    so,
    78% = 35%+ 45% - both
    both = 2%


    600 of 2%
    = 12

  2. Omkar Indapure
    Omkar Indapure :
    4 years ago

    How 22% came?

  3. Abhilasha Thakur
    Abhilasha Thakur :
    5 years ago

    45% failed in chem => 55% passed in chem
    35% failed in pay => 65% passed in pay

    now, 55% of 600 passed in chem => 55/100*600 = 330
    from question, 40% of those who passed in chem(i.e 330) also passed in pay => 40/100 *330 = 132 , so, 132 students passed in both
    so % who passed in both = 132/600*100 = 22%
    so, % of student who passed in any of the physics or chem or both (65% +55% -22%) =98%
    so, the % of students who are failed in both =2% => 2/100*600 =>12

  4. Anji
    Anji :
    6 years ago

    it is given that 40% of the students passed in both the subject how are u taking 22%

  5. Anji
    Anji :
    6 years ago

    it is given that 40% of the students passed in both the subject how are u taking 22%

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