CAT 2015 Quantitative Ability

There are a total of 78 B-schools that place their students
∴ No. of B-schools which are reputed and place their students = $\frac{1}{6}\times 78=13$
Let No. of B-schools that are recognised = x
∴ No. of recognised B-schools that place their students = $\frac{1}{4}\mathit{x}$
∴No. of recognised B-schools that do not place their students = $\frac{3\mathit{x}}{4}$
∴ $\frac{3\mathit{x}}{4}=39\Rightarrow \mathit{x}=52$
Out of 13 reputed B-schools, 6 are recognised too
∴ Number of B-schools that are either recognised and place their students or reputed and place their students
$=13+13-6=20$
∴ Number of B-school that are neither reputed nor recognised but place their students $=78-20=58$ .