CAT 2017

Slot 2

QA

Question & Solution

$\frac{1}{a}+\frac{1}{b}=\frac{1}{9}$
=> $ab = 9(a + b)$
=> $ab - 9(a+b) = 0$
=> $ab - 9(a+b) + 81 = 81$
=> $(a - 9)(b - 9) = 81, a > b$
Hence we have the following cases,
$a - 9 = 81, b - 9 = 1$ => $(a,b) = (90,10)$
$a - 9 = 27, b - 9 = 3$ => $(a,b) = (36,12)$
$a - 9 = 9, b - 9 = 9$ => $(a,b) = (18,18)$
Hence there are three possible positive integral values of (a,b)