Question

difference of 25 years between the ages of a father and his son. After 10 years the sons age will be half of his fathers age find their present age

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Answer 1

• Let the father's present age be x.

• Let the present age of his son be y.

By data,

Difference between the ages of father and son is 25.

x - y = 25

Let the above equation be equation 1.

• Let the father's age after 10 years be x + 10

• Let the son's age after 10 years be y + 10

Again by data,

After 10 years the son's age will be half of his fathers age.

$y + 10 = \frac{1}{2} (x + 10) \\ \\ 2(y + 10) = x + 10 \\ \\ 2y + 20 = x + 10 \\ \\ 20 - 10 = x - 2y \\ \\ 10 = x - 2y \\ \\ x - 2y = 10$

Let the above equation be equation 2.

Subtracting equation 2 from equation 1.

$(x - y ) - (x - 2y)= 25 - 10 \\ \\ x - y - x + 2y = 15 \\ \\ 2y - y = 15 \\ \\ y = 15$

The present age of the son is 15.

Substitute y = 15 in any one of the equation.

Let's put y = 15 in equation 1.

$x - y = 25 \\ \\ x - 15 = 25 \\ \\ x = 25 + 15 \\ \\ x = 40$

The present age of father is 40.

Answer 2

Let the father's present age be x.

Let the present age of his son be y.

By data,

Difference between the ages of father and son is 25.

x - y = 25

Let the above equation be equation 1.

Let the father's age after 10 years be x + 10

Let the son's age after 10 years be y + 10

Again by data,

After 10 years the son's age will be half of his fathers age.

1y+10=2/ 1 (x+10)

2(y+10)=x+10

2y+20=x+10

20−10=x−2y

10=x−2y

x−2y=10

Let the above equation be equation 2.

Subtracting equation 2 from equation 1.

(x−y)−(x−2y)=25−10

x−y−x+2y=15

2y−y=15

y=15

The present age of the son is 15.

Substitute y = 15 in any one of the equation.

Let's put y = 15 in equation 1.

x−y=25

x−15=25

x=25+15

x=40

The present age of father is 40.