Question

6 yrs ago the age of a is double of b if the ratio of their present age is 4:3 find the present age of b

Answer 1

let present age of A = x

let present age of B = y

x/y = 4/3

⇒ 3x = 4y

⇒ 3x - 4y = 0   --------------------------eq1

SIX YEARS AGO

Age of A = x - 6

Age of B =  y - 6

given (x-6) = 2 × (y-6)

⇒ x -6 = 2y - 12

⇒ x - 2y = -12 + 6

⇒ x - 2y = -6   -------------------------------------eq2

now we have following two equation to solve.

3x - 4y = 0   --------------------------eq1

x - 2y = -6   ---------------------------eq2

multiplying eq 2 by 2

3x - 4y = 0   --------------------------eq1

2x - 4y = -12   ------------------------eq3

subtracting eq3 from eq1

⇒ 3x - 2x -4y + 4y = 0 - (-12)

⇒ x = 12

from eq 1

3× 12 - 4y = 0  

⇒ -4y = -36

⇒ y = 9

hence present age of b = y = 9 years