Question

the age of A is five years more than that of B . 5 years ago the ratio of their ages was 3:2 .find their present ages​

Answer 1

Given:-

• The age of A is five years more than that of B
• 5 years ago the ratio of their ages was 3:2.

To find:-

• Find present ages ?

Solutions:-

• Let the age of A be 'x' years.
• Let the age of B be 'y' years.

The age of A is five years more than that of B

=> x = y + 5 ........(i).

5 years ago the ratio of their ages was 3:2

A's age = (x - 5) years

B's age = (y - 5) years

According to question:-

=> (x - 5)/(y - 5) = 3/2

=> 2(x - 5) = 3(y - 5)

=> 2x - 10 = 3y - 15

=> 2x - 3y = -15 + 10

=> 2x - 3y = -5

Putting the value of 'x' from equation (i)

=> 2x - 3y = -5

=> 2(y + 5) - 3y = -5

=> 2y + 10 - 3y = -5

=> 2y - 3y = -5 - 10

=> -y = -15

=> y = 15

Putting the value of 'y' in equation (i).

=> x = y + 5

=> x = 15 + 5

=> x = 20

Now,

• A's age = x = 20 years
• B's age = y = 15 years

Hence, the present ages of A and B are 20 years and 15 years.