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 :

Answer: Option D

Result	Physics	Chemistry
Failed	35%	45%
Passed	65%	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