Answer: 500 students

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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