Mathematics
In a city, there are 25 Hindi medium schools, 18 English medium schools and 7 schools have both the mediums. Find
(i) how many schools are there in all in the city ;
(ii) how many schools have Hindi medium only ;
(iii) how many schools have English medium only.
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Answer
Given:
Total Hindi medium schools: n(H) = 25
Total English medium schools: n(E) = 18
Schools with both mediums: n(H ∩ E) = 7
(i) how many schools are there in all in the city
This represents the union of the two sets, n(H ∪ E).
We know the formula:
n(H ∪ E) = n(H) + n(E) - n(H ∩ E)
Substituting the values in above, we get:
n(H ∪ E) = 25 + 18 - 7
n(H ∪ E) = 43 - 7
n(H ∪ E) = 36
∴ There are 36 schools in all in the city.
(ii) how many schools have Hindi medium only
This represents the set H - E, consisting of schools that are Hindi medium but not English medium.
We use the formula:
n(H - E) = n(H) - n(H ∩ E)
Substituting the values in above, we get:
n(H - E) = 25 - 7
n(H - E) = 18
∴ 18 schools have Hindi medium only.
(iii) how many schools have English medium only.
This represents the set E - H, consisting of schools that are English medium but not Hindi medium.
We use the formula:
n(E - H) = n(E) - n(H ∩ E)
Substituting the values in above, we get:
n(E - H) = 18 - 7
n(E - H) = 11
∴ 11 schools have English medium only.
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