Question

the sum of the ages of a father and his son is 50 years five years ago the product of their ages 175 find a present age

Answer 1

Let the present of father be x years.

So, present age of his son = 50-x years.

Now, According to question,

(x-5)(50-x-5)=175

(x-5)(45-x)=175

45x-x2-225+5x=175

50x-x2=175+225

⇒x2-50x+400=0

x2-40x-10x+400=0

x(x-40)-10(x-40)=0

(x-40)(x-10)=0

put x-40=0 and x-10=0

x=40 , x=10

Now, rejecting x=10 because age of father can't be less than his son, we get

x=40

Hence, Present age of father = 40 years.

Present age of his son = 50-10=40 years.----Ans.

Answer 2

Given:

The sum of the ages of a father and his son is 50 years. Five years ago, the product of their ages was 175.

To find:

The present age of father and son.

Solution:

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

So, according to the question, we have,

$x + y = 50 \: years \: \: (i)$

Five years ago, the age of father = x - 5 years

Five years ago, the age of son = y - 5 years

So, according to the question, we have,

$(x - 5) \times (y - 5) = 175 \: \: (ii)$

From (i) we have,

$y = 50 - x$

On putting the value of y in (ii), we have,

$(x - 5)(50 - x - 5) = 175$

$(x - 5)(45 - x) = 175$

$- {x}^{2} + 45x - 225 + 5x = 175$

$- {x}^{2} + 50x - 400 = 0$

${x}^{2} - 50x + 400$

After splitting the middle term, we have,

${x}^{2} - 40x - 10x + 400 = 0$

$x(x - 40) - 10(x - 40) = 0$

$(x - 10)(x - 40) = 0$

$x = 10 \: and \: x = 40$

Now, as the age of the father cannot be less than the son, so, after ignoring x = 10, we have,

age of the father = 40 years

On putting the value of x in (i), we have,

The present age of son:

$y = 50 - 40 = 10 \: years$

Hence, the present ages of father and son are 40 years and 10 years respectively.