Management Aptitude Test 2017 Paper

(c) 6
Let the two integers be x and 10 - x .
According to the question,
$\frac{1}{\mathit{x}}+\frac{1}{10-\mathit{x}}=\frac{5}{12}$
⇒ $\frac{10-\mathit{x}+\mathit{x}}{\mathit{x}\left(10-\mathit{x}\right)}=\frac{5}{12}$
⇒ $\frac{10}{\mathit{x}\left(10-\mathit{x}\right)}=\frac{5}{12}$
120 = 5x(10 - x)
⇒ 5${\mathit{x}}^2$ -50 x + 120 = 0
⇒ ${\mathit{x}}^2$ - 10x + 24 = 0
⇒ ${\mathit{x}}^2$ - 6x - 4x + 24 = 0
⇒ x (x - 6 ) - 4 (x - 6 ) = 0
⇒ (x - 4 )(x - 6 ) = 0
⇒ x = 4, 6
Value of larger integer is 6.