Let the two numbers be : P and Q
Given - The Two numbers are in the ratio 5 : 3
[tex]:\implies \mathsf{\dfrac{P}{Q} = \dfrac{5}{3}}[/tex]
[tex]:\implies \mathsf{P = \dfrac{5Q}{3}}[/tex]
Given : The Difference of two numbers is 18
[tex]:\implies[/tex] P - Q = 18
Substituting the value of P in the above Equation, We get :
[tex]:\implies \mathsf{\dfrac{5Q}{3} - Q = 18}[/tex]
[tex]:\implies \mathsf{\dfrac{5Q - 3Q}{3} = 18}[/tex]
[tex]:\implies \mathsf{\dfrac{2Q}{3} = 18}[/tex]
[tex]:\implies \mathsf{\dfrac{Q}{3} = 9}[/tex]
[tex]:\implies \mathsf{Q = 27}[/tex]
Substituting the value of Q in Equation P - Q = 18, We get :
[tex]:\implies[/tex] P - 27 = 18
[tex]:\implies[/tex] P = 27 + 18
[tex]:\implies[/tex] P = 45
Answer : The Two Numbers are : 45 and 27
