Question

3. The ratio of the ages of a father and his son 10 years
from now would be 5:3, while 10 years ago, it was
3:1. What is the ratio of the age of son to that of father
today?​

Answer 1

Question:

The ratio of the ages of a father and his son is 10 years from now would be 5:3 and 10 years ago it was 3:1. What is the ratio of the age of son to that of father today?

Answer:

The ratio of father's and son's present age is 40:20 or 2:1 .

OR ,

The ratio of son's and father's present age is 1:2 .

Solution:

Let the present age of father be "x" and the present age of son be "y" .

Father's age after 10 years = (x+10) yrs

Son's age after 10 years = (y+10) yrs

According to the question,

The ratio of the father's age and the son's age after 10 years will be 5:3 .

=> (x+10):(y+10) = 5:3

=> (x+10)/(y+10) = 5/3

=> 3(x+10) = 5(y+10)

=> 3x + 30 = 5y + 50

=> 3x - 5y = 50 - 30

=> 3x - 5y = 20 -----------(1)

Also,

Father's age 10 years ago = (x-10) yrs

Son's age 10 years ago = (y-10) yrs

According to the question,

The ratio of the father's age and the son's age 10 years ago was 3:1.

=> (x-10):(y-10) = 3:1

=> (x-10)/(y-10) = 3/1

=> x - 10 = 3(y-10)

=> x - 10 = 3y - 30

=> x = 3y - 30 + 10

=> x = 3y - 20 -------(2)

Now,

Putting x = 3y - 20 in eq-(1) , we get;

=> 3x - 5y = 20

=> 3(3y-20) - 5y = 20

=> 9y - 60 - 5y = 20

=> 9y - 5y = 20 + 60

=> 4y = 80

=> y = 80/4

=> y = 20

Now,

Putting y = 20 in eq-(2) , we get;

=> x = 3y - 20

=> x = 3•20 - 20

=> x = 60 - 20

=> x = 40

Hence,

The present age of father is 40 years and the present age of son is 20 years.

Also,

The ratio of father's and son's present age is 40:20 or 2:1 .

OR ,

The ratio of son's and father's present age is 1:2 .

Answer 2

Answer:

→ 40 years and 20 years or in ratio 40 : 20 / 2 : 1.

Explanation:

→ Let M be the father's age.

→ Let N be the son's age.

→ (M + 10) = father's age after 10 years.

→ (N + 10) = son's age after 10 years.

Hence, 10 years = 5 : 3

→ (M + 10) : (N + 10) = 5 : 3

→ (N + 10) / (N + 10) = 5 / 3

→ 3 (M + 10) = 5 (N + 10)

→ 3M + 30 = 50N + 50

→ 3M - 5N = 50 - 30

→ 3M - 5N = 20 Equation (1)

→ M - 10 = father's age after 10 years.

→ N - 10 = son's age after 10 years.

Hence, 10 years = 3 : 1

→ (M - 10) : (N - 10) = 3 : 1

→ (M - 10) / (N - 10) = 3 / 1

→ M - 10 = 3(N -10)

→ M - 10 = 3N - 30

→ M = 3N - 30 + 10

→ M = 3N - 20 Equation (2)

Adding (x = 3y - 20) for Equation (1)

→ 3M - 5N = 20

→ 3 (3N - 20) - 5N = 20

→ 9N - 60 - 5N = 20

→ 9N - 5N = 20 + 60

→ 4N = 80

→ N = 80/4

→ N = 20

Adding (y = 20) for Equation (2)

→ M = 3N - 20

→ M = 3 × 20 - 20

→ M = 60 - 20

→ M = 40

1. Therefore , 40 and 20 is the age of father and son and
2. 40 , 20 years or in ratio 40 : 20 or 2 : 1.