Solution:
Let U be the set of those students who appeared in the examination and were
surveyed.
Let M and E be the sets of students who passed in Mathematics and English,
respectively.
Given,
n(U) = 100%
n(M) = 80%
n(E) = 75%
n(\overline{M \cup E}) = 5%
n(M \cap E) = 300
Using formula,
n(U) = n(M) + n(E) - n(M \cap E) + n(\overline{M \cup E})
or, 100% = 80% + 75% - n(M \cap E) + 5%
or, n(M \cap E) = 160% - 100%
\therefore n(M \cap E) = 60%
We know,
n(M \cap E) = 55% of n(U)
or, 300 = \frac{60}{100} × n(U)
or, \dfrac{300 × 100}{60} = n(U)
\therefore n(U) = 500
Hence, the required number of students whose results were
surveyed is 500.
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