Question

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​

Answer 1

Here is your answer.

Answer 2

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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