Question

The present ages of two children are in the ratio 2:3 .Five years ago, the ratio of their ages was 1:2 .Find their present ages.​

Answer 1

Answer:

Present ages are 10 and 15 years

Step-by-step explanation:

Let the age of two children are 2x and 3x which is in the given ratio that is

2x : 3x = 2 : 3

NOW

five year ago their ages are

2x - 5 and 3x - 5

and

According to given condition

2x - 5 : 3x - 5 = 1 : 2

⇒ (2x - 5) / (3x - 5) = 1/2

⇒ 2×(2x - 5) = 1×(3x - 5)

⇒ 4x - 20 = 3x - 15

⇒ 4x -3x = 20 - 15 = 5

⇒       x = 5

So

The present ages are

2x = 2(5) = 10 years

3x = 3(5) = 15 years

Thus

Present ages are 10 and 15 years

Answer 2

Given:  ratio 2:3 , five years ago ratio was 1:2

To find: present ages

Solution:

• To find the present ages, let the common ratio be z.

• So the age of two children are 2z and 3z

• Now, five year ago their ages were

                2z - 5 and 3z - 5

• So question says Five years ago, the ratio of their ages was 1:2,
• So computing both, we get:

               2z - 5 : 3z - 5 = 1 : 2

               (2z - 5) / (3z - 5) = 1/2

               2×(2z - 5) = 1×(3z - 5)

               4z - 20 = 3z - 15

               4z -3x = 20 - 15 = 5

                z = 5

• So the present ages of the two children are:

                2z = 2(5) = 10 years

                3z = 3(5) = 15 years

Answer:

• Present ages are 10 and 15 years.