Question

In an examination, 56% of the candidates failed in english and 48% failed in science. if 18% failed in both english and science, find the percentage who passed in both the subjects.

Answer 1

Ans is in attachment

Answer 2

Let Total candidates = 100

Number of candidates failed

in English =n(E) = 56

Number of candidates failed

in Science =n(S) = 48

Number of candidates failed in

both the subjects =n(EnS)= 18

Now ,

Number of candidates failed = n(EUS)

_________________________

We know that,

If A and B are two sets

n(AUB) = n(A)+n(B)-n(AnB)

__________________________

Here,

n(EUS) = n(E)+n(S)-n(EnS)

= 56 + 48 - 18

= 104 - 18

= 86

Now ,

Number of passed candidates

= Total candidates - n(EUS)

= 100 - 86

= 14

Therefore,

Percentage of candidates who

passed both the subjects = 14%

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