At a particular university with 200 students 40% receive loans and 30%

• Total number of students in the university \(= 200\).
• Let us consider these \(200\) students in the university as \(100\) %.

o \(40\)% of the students received loans.
o \(30\)% of the students received scholarships.

• Using the above information, we can draw the Venn diagram as shown –

• \(X + Z = 40\)%
• \(Y + Z = 30\)%
• \(X + Y + Z + W = 100\)%
• where \(W\) is the percentage of students who received neither loans nor scholarships.
• And we need to find the value of \(W\) = ?

• It is given that at least twenty-five percent of the students do not receive loans.
• This means that \(Y + W ≥ 25\)%.
• But we cannot find the exact value of \(W\) using the above information.

• It is given that twenty-five percent of the students receive both loans and scholarships.
• This means that \(Z = 25\)%
• Using the above information, we can find the value of \(X\) and then subsequently the value of \(W\).

o \(X + Z = 40\)%

• \(X = 15\)%
o \(X + Y + Z + W = 100\)%

• \(15\)% \(+ 30\)%\(+ W = 100\)%
• \(W = 55\)%

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