Question

The ratio of the ages of Raj and Answers is 3:4. After 4 years the ratio of there ages will be 4:5. Find there ages.

Answer 1

GIVEN:

The ratio of the ages of Raj and Anu is 3:4

Let the ages be 3x and 4x

After 4 years:

Their ages will be 3x + 4 and 4x + 4

The ratio of their ages after 4years = 4:5

According to the problem,

3x + 4 / 4x + 4 = 4/5

5(3x + 4) = 4(4x + 4)

15x + 20 = 16x + 16

20 - 16 = 16x - 15x

=> x = 4

Raj's present age:

3x = 3(4) = 12 years.

Anu's present age:

4x = 4(4) = 16 years

Therefore, the ages of Raj and Anu are 12 years and 16 years respectively.

Answer 2

Answer :-

The ages of Raj and Answers are 12 years and 16 years respectively.

Solution :-

Ratio of the ages of Raj and Answers = 3 : 4

Consider the ages of Raj and Answers as 3x and 4x respectively

After 4 years

Age of Raj = 3x + 4

Age of Answers = 4x + 4

Ratio of the ages of Raj and Answers after 4 years = 4 : 5

According to the question :-

$\\ \sf \longrightarrow \dfrac{3x + 4}{4x + 4} = \dfrac{4}{5} \\ \\ \\ \sf \longrightarrow 5(3x + 4) = 4(4x + 4) \\ \\ \\ \sf \longrightarrow 15x + 20 = 16x + 16 \\ \\ \\ \sf \longrightarrow 20 - 16 = 16x - 15x \\ \\ \\ \sf \longrightarrow 4 = x \\ \\ \\ \sf \longrightarrow x = 4$

Age of Raj = 3x = 3(4) = 12 years

Age of Answers = 4x = 4(4) = 16 years

Therefore the ages of Raj and Answers are 12 years and 16 years respectively.