Question

please answer fastpls​

Answer 1

A's present age = 19 years

B's present age = 15 years

Solution

Let the present age of A be x years and the present age of B be y years .

Then , three years ago ;

A's age = (x-3) years

B's age = (y-3) years

Also, three years hence ;

A's age = (x+3) years

B's age = (y+3) years

According to the question;

Three years ago, the ratio of the ages of A and B was 4:3.

Thus;

=> (x-3):(y-3) = 4:3

=> (x-3)/(y-3) = 4/3

=> 3•(x-3) = 4•(y-3)

=> 3x - 9 = 4y - 12

=> 3x - 4y = 9 - 12

=> 3x - 4y = - 3 --------(1)

Also;

Three years hence, the ratio of ages of A and B will be 11:9.

Thus;

=> (x+3):(y+3) = 11:9

=> 9•(x+3) = 11•(y+3)

=> 9x + 27 = 11y + 33

=> 9x - 11y = 33 - 27

=> 9x - 11y = 6 ---------(2)

Now,

Multiplying both sides of eq-(1) , we get;

=> 3•(3x - 4y) = 3•(- 3)

=> 9x - 12y = - 9 ---------(3)

Now,

Subtracting eq-(3) from eq-(2) , we get;

=> (9x - 11y) - (9x - 12y) = 6 - (- 9)

=> 9x - 11y - 9x + 12y = 6 + 9

=> y = 15

Now,

Putting y = 15 in eq-(1) , we get;

=> 3x - 4y = - 3

=> 3x = 4y - 3

=> 3x = 4•15 - 3

=> 3x = 60 - 3

=> 3x = 57

=> x = 57/3

=> x = 19

Hence,

A's present age = x years = 19 years

B's present age = y years = 15 years

Answer 2

Hope this helps you ;)

Question:

Three years ago, the ratio of the ages of A and B was 4:3. Three years hence, the ratio of their ages will be 11:9. Find the present ages of A and B.

Answer:

A's present age = 19 years

B's present age = 15 years

Solution:

Let the present age of A be x years and the present age of B be y years .

Then , three years ago ;

A's age = (x-3) years

B's age = (y-3) years

Also, three years hence ;

A's age = (x+3) years

B's age = (y+3) years

According to the question;

Three years ago, the ratio of the ages of A and B was 4:3.

Thus;

=> (x-3):(y-3) = 4:3

=> (x-3)/(y-3) = 4/3

=> 3•(x-3) = 4•(y-3)

=> 3x - 9 = 4y - 12

=> 3x - 4y = 9 - 12

=> 3x - 4y = - 3 --------(1)

Also;

Three years hence, the ratio of ages of A and B will be 11:9.

Thus;

=> (x+3):(y+3) = 11:9

=> 9•(x+3) = 11•(y+3)

=> 9x + 27 = 11y + 33

=> 9x - 11y = 33 - 27

=> 9x - 11y = 6 ---------(2)

Now,

Multiplying both sides of eq-(1) , we get;

=> 3•(3x - 4y) = 3•(- 3)

=> 9x - 12y = - 9 ---------(3)

Now,

Subtracting eq-(3) from eq-(2) , we get;

=> (9x - 11y) - (9x - 12y) = 6 - (- 9)

=> 9x - 11y - 9x + 12y = 6 + 9

=> y = 15

Now,

Putting y = 15 in eq-(1) , we get;

=> 3x - 4y = - 3

=> 3x = 4y - 3

=> 3x = 4•15 - 3

=> 3x = 60 - 3

=> 3x = 57

=> x = 57/3

=> x = 19

Hence,

A's present age = x years = 19 years

B's present age = y years = 15 years