Discussion
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500.
The number of students who like their core branches is
Answer: A
The number who like their core branches is 1,800.
Of the 10,000 students, \(10000 - 1500 = 8500\) like at least one kind of branch. Let \(C\) like their core branches and \(O\) like other branches, with \(C = O/4\) and 500 liking both. By inclusion and exclusion,
\[ \begin{aligned} C + O - 500 &= 8500 \\ C + 4C &= 9000 \\ C &= 1800 \end{aligned} \]
So 1,800 like their core branches and 7,200 like other branches. 1,600 comes from subtracting the 500 who like both instead of adding it back (\(5C = 8000\)), and 3,500 and 1,500 are numbers from the question rather than results.
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