Question

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present age.

Answer 1

✬ Father's age = 36 years ✬

✬ Son's age = 9 years ✬

Step-by-step explanation:

Given:

• Sum of ages of father and son is 45 years.
• Five years ago product of their ages was 124.

To Find:

• What are the present ages of both ?

Solution: Let father's age be x years. Then

➼ Present age of son = (45 – x)

[ 5 years ago their ages were ]

• Father's age = (x – 5) years
• Son's age = (45 – x – 5) = (40 – x) years

Now, A/q

• Product of ages is 124.

$\implies{\rm }$ (x – 5) (40 – x) = 124

$\implies{\rm }$ x(40 – x) –5(40 – x) = 124

$\implies{\rm }$ 40x – x² – 200 + 5x = 124

$\implies{\rm }$ 45x – x² = 124 + 200

$\implies{\rm }$ 45x – x² = 324

$\implies{\rm }$ 0 = x² – 45x + 324

Now, break this by middle term splitting method.

➱ x² – 45x + 324

➱ x² – 36x – 9x + 324

➱ x (x – 36) –9 (x – 36)

➱ (x – 9) (x – 36)

➱ (x – 9) = 0 or, (x – 36) = 0

➱ x = 9 or x = 36

Father's age cannot be 9 years so we will take x = 36 years.

So,

➬ Father's age = x = 36 years

➬ Son's age = 45 – x = 45 – 36 = 9 years.

Answer 2

$\huge\bold\blue{Answer:}$

Let the present age of son = x

So, the present age of father = 45 - x

5 years ago,

Age of son = x - 5

and age of the father = 45 - x - 5 = 40 - x

Now, product of their ages = 124

=> (x - 5)*(40 - x) = 124

=> 40x - x2 - 5 * 40 + 5x = 124

=> 40x - x2 - 200 + 5x = 124

=> 45x - x2 - 200 = 124

=> 45x - x2 - 200 - 124 = 0

=> 45x - x2 - 324 = 0

=> x2 - 45x + 324 = 0

=> x2 - 36x - 9x + 324 = 0

=> x(x - 36) - 9(x - 36) = 0

=> (x - 36)*(x - 9) = 0

=> x = 9, 36

If the present age of son is 9 years

then present age of father = 45 - 9 = 36 years

Again, if the present age of son is 36 years

then present age of father = 45 - 36 = 9 years

which is not possible.

So, the present age of son is 9 years and the present age of the father is 36 years.