Question

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

Answer 1

Answer:

The present ages of the children are 10 and 15 years.

Step-by-step explanation:

Given :

Present age ratio = 2 : 3

Ratio of ages 5 years back = 1 : 2

To find :

Their present ages

Solution :

Let the present age be -

• One as 2x
• Second as 3x

$\sf{\longrightarrow} \: \frac{2x - 5}{3x - 5} = \frac{1}{2} \\ \\ \sf{\longrightarrow} \: 2(2x - 5) = 1(3x - 5) \\ \\ \sf{\longrightarrow} \: 4x - 10 = 3x - 5 \\ \\ \sf{\longrightarrow} \: 4x - 3x = - 5 + 10 \\ \\ \sf{\longrightarrow} \: x = 5$

★ Value of 2x

$\sf{\longrightarrow} \: 2(5) \\ \\ \sf{\longrightarrow} \: 10$

One child's age = 10 years

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\longrightarrow} \: 3(5) \\ \\ \sf{\longrightarrow} \: 15$

Another child's age = 15 years

$\therefore$ The present ages of the children are 10 and 15 years.

Answer 2

Answer:

Step-by-step explanation:

Given :-

The present age of two children are in the ratio 2:3.

Five year ago the ratio of their ages was 1:2.

To Find :-

Their Present ages.

Solution :-

Let the age of two children are 2x : 3x.

According to the Question

Five year ago their ages are

2x - 5 and 3x - 5

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

⇒ (2x - 5) / (3x - 5) = 1/2

    [Cross Multiplication]

⇒ 2 (2x - 5) = 1 (3x - 5)

⇒ 4x - 20 = 3x - 15

⇒ 4x - 3x = 20 - 15 = 5

⇒  x = 5

The present age of 1st children =  2x = 2(5) = 10 years

The present age of 2nd children =  3x = 3(5) = 15 years

Hence, the present ages of two children are 10 and 15 years.