Question

8. The ages of Sophie and Jessie are in the ratio 4:5. Four years from now the ratio of their ages will be 6:7.
Find their present ages.
​

Answer 1

let, the present age of Sophie be x years.

the present age of Jessie is y years.

a/c to condition 1

x:y=4:5

x = 4

y 5

by c.m.,

5x=4y

5x-4y=0______1

after 4 years,

sophie age will be (x+4) year's.

Jessie age will be (y+4) year's.

a/c to condition 2

(x+4):(y+4)=6:7

(x+4) =6

(y+4) 7

by c.m.,

(x+4)×7=(y+4)×6

7x+28=6y+24

7x-6y=24-28

7x-6y=-4_____2

by solving the equation we get,

x=8 and y=10

therefore,

the present age of Sophie is 8 years.

the present age of Jessie is 10 years.

Answer 2

Sophie's present age = 8 years

Jessie's present age = 10 years

Solution:

We are given that the present ages of Sophie and Jessie are in the ratio 4:5. From this, let us assume:

⇒ Sophie's present age = 4x

⇒ Jessie's present age = 5x

After 4 years from their present ages, their ratio of ages become 6:7. Let their ages after 4 years from their present ages be 6x and 7x respectively.

According to the question:

⇒ (4x + 4)/(5x + 4) = 6x/7x

⇒ 7x(4x + 4) = 6x(5x + 4)

⇒ 28x² + 28x = 30x² +24x

⇒ 28x² - 30x² = 24x - 28x

⇒ - 2x² = - 4x

⇒ x² = 2x

⇒ x = 2

We know that,

⇒ Sophie's present age = 4x

⇒ Sophie's present age = 4 × 2

⇒ Sophie's age = 8 years

Also,

⇒ Jennie's present age = 5x

⇒ Jennie's present age = 5 × 2

⇒ Jennie's present age = 10 years

Hence, their present ages are 8 and 10 years respectively.