Let the two numbers be 19 x and 24 x . When each number is reduced by 36 , the ratio becomes:
19x−36
24x−36
=
3
4
Cross-multiplying, we get: 4(19x−36)=3(24x−36) ⇒76x−144=72x−108 ⇒76x−72x=144−108 ⇒4x=36 ⇒x=9 Now, the two numbers are: 19x=19×9=171 24x=24×9=216 The sum of the numbers =171+216=387