600 students took the test on physics and chemistry. 35% students failed in physics

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

(a) 138

(b) 230

(c) 60

(d) None of these

Solution - 

Total number of students who took test = 600

Students who failed in physics = 35%

Students who passed in physics = 65%

Students who failed in chemistry = 45%

Students who passed in chemistry = 55%

so,

Students who passed in chemistry = 55% of 600

= (55/100) × 600

= 330

Students who passed in chemistry also passed in physics = 40% 

= 40% of 330

= (40/100) × 330

=132

Therefore,

No. of students who passed in both = 132

percentage of students who passed in both  = (132/600) × 100

percentage of students who passed in both  = 22%

Passed in both = 22% of total student

Percentage of students who passed in any of physics or chemistry or both = (65 + 55) -2 = 98%

Thus,

The percentage of students who failed in both = 100% - 98% = 2%

Therefore,

The total no. of students who failed in both = 2% of 600

= (2/100) × 600

= 12

Hence,

The total no. of students who failed in both = 12.