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there are 11 illiterate males in the group.
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Let total students be x.
Let no. of students passing in maths be M and no. of students passing english be E. We will used the formula:
n(M ∪ E) = n(M) + n(E) - n(M ∩ E)
70% of x passed in English. This means n(E) = 7x/10
65% of x passed in Maths. This means n(M) = 13x/20
27% of x failed in both. This means n((M ∪ E)') = 27x/100, which further implies n(M ∪ E) = 1 - 27x/100 = 73x/100
248 passed in both, which means n(M ∩ E) = 248
Applying the formula,
73x/100 = 7x/10 + 13x/20 - 248
⇒ 248 = 27x/20 - 73x/100 = 62x/100
⇒ x = 400
Total number of students is 400.
I hope you know the meanings of the symbols.
Let no. of students passing in maths be M and no. of students passing english be E. We will used the formula:
n(M ∪ E) = n(M) + n(E) - n(M ∩ E)
70% of x passed in English. This means n(E) = 7x/10
65% of x passed in Maths. This means n(M) = 13x/20
27% of x failed in both. This means n((M ∪ E)') = 27x/100, which further implies n(M ∪ E) = 1 - 27x/100 = 73x/100
248 passed in both, which means n(M ∩ E) = 248
Applying the formula,
73x/100 = 7x/10 + 13x/20 - 248
⇒ 248 = 27x/20 - 73x/100 = 62x/100
⇒ x = 400
Total number of students is 400.
I hope you know the meanings of the symbols.
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