Question

six years ago the ratio of Ages of Karan and Arjun was 6:5,
4 years from now the ratio of their ages will be 11:10 .

find their present ages
​

Answer 1

Answer:-

Let the present age of Karan be x years and Arjun be y years.

Given:-

Six years ago, the ratio of their ages was 6 : 5.

Karan's age before 6 years = (x - 6) years.

Arjun's age before 6 years = (y - 6) years.

So,

⟹ (x - 6) / (y - 6) = 6/5

⟹ 5(x - 6) = 6(y - 6)

⟹ 5x - 30 = 6y - 36

⟹ 5x - 6y = - 36 + 30

⟹ 5x - 6y = - 6 -- equation (1)

Also given that,

After 4 years, the ratio of their ages will be 11 : 10.

So,

According to the above condition;

⟹ (x + 4) / (y + 4) = 11/10

⟹ 10(x + 4) = 11(y + 4)

⟹ 10x + 40 = 11y + 44

⟹ 10x - 11y = 44 - 40

⟹ 10x - 11y = 4 -- equation (2)

Now,

Multiply equation (1) by 2 and subtract equation (1) from equation (2).

⟹ 10x - 11y - 2(5x - 6y) = 4 - 2(- 6)

⟹ 10x - 11y - 10x + 12y = 4 + 12

⟹ y = 16

Substitute y = 16 in equation (1).

⟹ 5x - 6(16) = - 6

⟹ 5x - 96 = - 6

⟹ 5x = - 6 + 96

⟹ 5x = 90

⟹ x = 90/5

⟹ x = 18

∴

Present age of Karan = x = 18 years.

Present age of Arjun = y = 16 years.

Answer 2

Given :-

Six years ago the ratio of Ages of Karan and Arjun was 6:5,

4 years from now the ratio of their ages will be 11:10

To Find :-

Present ages

Solution :-

Let six years ago the ages be 6x and 5x

Now

6x + 6 + 4/5x + 6 + 4 = 11/10

6x + 10/5x + 10 = 11/10

10(6x + 10) = 11(5x + 10)

60x + 100 = 55x + 110

60x - 55x = 110 - 100

5x = 10

x = 10/5

x = 20

Age of  Karan = 6x + 6 = 18 years

Age of  Arjun = 5x + 6 = 16 years