the ages of A and B are in the ratio 2:3. six years ago, their ages were in the ratio 3:5 find their present ages
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Step-by-step explanation:
let the age of A be x and that of B be y years.
therefore according to first condition
x:y = 2:3
x/y= 2/3
3x=2y
3x -2y =0.....(1)
thus there ages six years ago will be,
(x-6) of A
(y-6) of B
thus according to second condition,
(x-6):(y-6)=3:5
x-6/y-6 = 3/5
5(x-6)=3(y-6)
5x - 30 = 3y-18
5x -3y=-18+30
5x -3y = 12.....(2)
multiply (1) and(2) by 5 and 3 respectively
we get,
15x -10y=0.......(3)
15x-9y =36.......(4)
subtract (3) and(4)
we get,
y =36
substitute y =36 in (1)
3x+2y= 0
3x +2(36)=0
3x +72=0
x=-72/3
x= - 24
but age is never negative
thus x=24
thus, age's of A and B are 24 years and 36 years respectively.
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