Question

4 years ago the ratio of the age of A and B bus 2 ratio 3 and after 4 years it became 7 ratio 5 find their percentage ​

Answer 1

Step-by-step explanation:

This is a basic algebra equation I ll try to simplify it -

Let the current age of A and B is X and Y resp.

and as there are two conditions mentioned in the question itself which gives us two equations-

1.Four years ago, the ratio of the age of A and B was 2:3

i.e, Four years in the past

age of A( Four years in the past)= Present age of A -4 years ;

age of A( Four years in the past)=X-4…………(eq 1).

age of B( Four years in the past)= Present age of B -4 years ;

age of B( Four years in the past)=Y-4…………(eq 2).

as it is mentioned in the form of ratio,we’ll try to put it as the sentence goes

The ratio of the age of A and B was 2:3 which gives us

{(age of A( Four years in the past)/age of B( Four years in the past)}=(X-4)/(Y-4)

i.e (X-4)/(Y-4) =2/3

now cross multiplication yields following eq

3X-12=2Y-8;

3X-2Y = 4…………(eq 3).

after four years it will become 5:7.

so going in the same manner

age of A( Four years in the future)= Present age of A+4 years ;

age of A( Four years in the future)=X + 4…………(eq 4).

age of B( Four years in the future)= Present age of B +4 years ;

age of B( Four years in the future)=Y+4…………(eq 5).

after four years the ratio will become 5:7.

{(age of A( Four years in the future)/age of B( Four years in the future)}=(X+4)/(Y+4)

i.e (X+4)/(Y+4) =5/7

now as usual cross multiplication yields following eq

7X+28=5Y+20;

7X-5Y =-8…………(eq 6).

now getting together eq 3 and 6-

3X-2Y = 4 ………..(multiplying with 5 so that Y term will be eliminated)

7X-5Y =-8…………(multiplying with 2 so that Y term will be eliminated)

which yields

15X-10Y = 20……..eq 7

14X-10Y =-16……….eq 8 (multiply by (-1) )

eq 8 becomes

-14X + 10Y = 16…….eq 9

getting together eq 7 and eq9 .

15X-10Y = 20

-14X + 10Y = 16

after subtracting eq 9 from eq 7 we get

X = 36 (PRESENT AGE OF A)

Putting X = 36 in eq 3

3X-2Y = 4

which becomes

3(36)-2Y = 4

108–4= 2Y

104= 2Y

Y=(104 / 2)

Y=52 (PRESENT AGE OF B)

we can cross check this py putting these values in eq. 1, 2 and 4,5 and get the ratio values