Question

five years ago A man was 7 times as old as his son 5 years hence the father will be three times as old as his son find their present age​

Answer 1

Answer:

40 years.

Step-by-step explanation:

Let Five years ago the age of son be x years and age of father be 7x years

Present age of son =x+5

Present age of father =7x+5

5 years later their age will (x+10) and (7x+10)

∴7x+10=3(x+10)

7x−3x=20

4x=20

x=5

So, the present age of son=x+5=5+5= 10 years

and the present age of father=7x+5=35+5= 40 years

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Answer 2

Answer:

$\red\bigstar$ Present age of the son = 10 years

$\red\bigstar$ Present age of the father = 40 years.

SOLUTION

Let us assume that five years ago the age of the son is 'x'.

Then,according to the question the father is 7 times as old as his son.

$\implies$ Age of father five years ago = 7x.

Present Ages

Present age of the son = x + 5 $\longrightarrow$ (1)

Present age of the father = 7x + 5 $\longrightarrow$ (2)

Five years hence ,

Age of son will be = x + 10

Age of father will be = 7x + 10

It is also said in the question that , 5 years hence the father will be three times as old as his son.

$\implies$ 7x + 10 = 3(x + 10)

$\implies$ 7x + 10 = 3x + 30

$\implies$ 7x - 3x = 30 - 10

$\implies$ 4x = 20

$\implies \sf x = \dfrac{20}{4}$

$\implies$ x = 5.

Now, let us substitute the value of x = 5 in (1) to find the present age of the son.

$\implies$ Present age of the son = x + 5

$\implies$ Present age of the son = 5 + 5

$\implies$ Present age of the son = 10 years.

Now, let us substitute the value of x = 5 in (2) to find the present age of the father.

$\implies$ Present age of the father = 7x + 5

$\implies$ Present age of the father = 7 × 5 + 5

$\implies$ Present age of the father = 35 + 5 = 40 years.