Out of 250 students who failed in an examination, it was revealed that 128 failed in mathematics,87 failed in physics and 134 failed in chemistry.31 failed in maths and physics,54 failed in chemistry and mathematics,30 failed in chemistry and physics.find how many candidates failed in: [a]in all the three subjects.[b]in mathematics but not in physics.[c] in chemistry but not in mathematics.[d]in physics but not in chemistry or in mathematics.[e]in chemistry or in mathematics but not in physics.
Answers
(a) 16 students failed in all three subjects.
(b) 97 students failed in mathematics but not in physics.
(c) 6 students failed in chemistry but not in mathematics.
(d) 42 students failed in physics but not in chemistry or in mathematics.
(e) 116 students in chemistry or in mathematics but not in physics.
Step-by-step explanation:
Let the no. of students who failed in all the three subjects be x
so,
no. of students who failed in maths only = 128 - (31 -x) - (54 - x) - x
= 43 + x
no. of students who failed in physics only = 87 - (31 - x) - (30 - x) - x
= 26 + x
no. of students who failed in chemistry only = 134 - (54 - x) - (30 - x) - x
= 50 + x
no. of students who failed in maths and chemistry but not in Physics = 54 - x
no. of students who failed in Maths and physics but not in chemistry = 31 - x
no. of students who failed in physics and chemistry but not in maths = 30 - x
Sum of these equations = x + 43 + x + 26 + x + 50 + x + (54 - x) + (31 - x) + (30 - x) = 250
so,
⇒ 234 + x = 250
⇒ x = 16
Thus,
a). 16 students failed in all three subjects.
b). 97 students(128 - 31) failed in mathematics but not in physics.
c) 6 students(134 - 128) failed in chemistry but not in mathematics.
(d) 42 students(87 - 31 - 30 + 16) failed in physics but not in chemistry or in mathematics.
(e) 116 students(= 128 + 87 − 31 − 54 − 30 + 16 = 116) in chemistry or in mathematics but not in physics.
Learn more: find the number of students who failed
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