. If twice the age of A is added to B's age, thesum is 45 and if twice

1.	. If twice the age of A is added to B's age, thesum is 45 and if twice the age of B is added toA's age, the sum is 30. Then the age of B is
Answer» Step-by-step EXPLANATION: $\bf{\underline{\underline\red{Given:-}}}$ If TWICE the age of A is added to B's age, the sum is 45. If twice the age of B is added to A's age, the sum is 30. $\bf{\underline{\underline\blue{To\:Find:-}}}$ The age of B $\bf{\underline{\underline\green{Solution:-}}}$ Let The present age of B = x And present age of A = y According to the 1st condition:- If twice the age of A is added to B's age, the sum is 45 $\rm \implies x + 2y = 45.....(i)$ According to the 2nd condition:- If twice the age of B is added to A's age, the sum is 30. $\rm \implies 2x + y = 30.....(ii)$ Multiplying equation (i) with 2 $\rm \implies 2(x + 2y = 45)$ $\rm \implies 2x + 4y = 90.....(iii)$ Subtracting equation (ii) from (iii) $\rm \implies (2x + 4y )- (2x + y) = 90 - 30$ $\rm \implies 2x + 4y - 2x - y = 60$ $\rm \implies3y = 60$ $\rm \implies y = \dfrac{60}{3} = 20$ Substituting y = 15 in equation (i) $\rm \implies x + 2y = 45$ $\rm \implies x + 2(20) = 45$ $\rm \implies x +40 = 45$ $\rm \implies x = 45 - 5$ $\rm \implies x = 5$ $\boxed{ \rm \therefore Present \: age \: of \: B = 5years}$