Question

The ratio between the ages of Amar and Kabir is 3:4 at present.after 4 years ago their ages would be 7:9.ratio of ages of Kabir and amar after 20 years from now?​

Answer 1

`Ratio = 11:13`

Explanation:

Represent Amar age with x

Represent Kabir age with y

So, we have:

Presently

`x : y = 3 : 4`

After 4 years

`x + 4 : y + 4 = 7 : 9`

Simplify both ratios:

`x : y = 3 : 4`

`(x)/(y) = (3)/(4)`

Cross Multiply

`4x = 3y`

Make x the subject

`x = (3)/(4)y`

`x + 4 : y + 4 = 7 : 9`

`(x + 4)/(y + 4) = (7)/(9)`

Cross Multiply

`7(y+4) = 9(x+4)`

Open Brackets

`7y + 28 = 9x + 36`

Collect Like Terms

`9x = 7y + 28 - 36`

`9x = 7y -8`

Substitute
`(3)/(4)y` for x in
`9x = 7y -8`

`9((3)/(4)y) = 7y - 8`

`(27)/(4)y = 7y - 8`

`6.75y = 7y - 8`

`6.75y - 7y = - 8`

`-0.25y = - 8`

`y = -8/-0.25`

`y = 32`

Substitute 32 for y in
`x = (3)/(4)y`

`x = (3)/(4) * 32`

`x = (3* 32)/(4)`

`x = (96)/(4)`

`x = 24`

So, in 20 years time, the ratio of the ages would be:

`x + 20 : y + 20`

This gives

`24 + 20 : 32 + 20`

`44 : 52`

Divide by 4

`44/4:52/4`

`11:13`

Hence, the Ratio is

`Ratio = 11:13`