Question

27. Two years ago, a man was five times as old as his son. Two years later,
his age will be 8 more than three times the age of the son. Find the
present ages of the man and his son.
​

Answer 1

◙ Given ◙

• Two years ago, a man was five times as old as his son.

• Two years later,  his age will be 8 more than three times the age of the son.

◙ To find ◙

The present ages of the man and his son.

◙ Solution ◙

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

A/q, 2 years ago,

(y - 2) = 5(x - 2)

⇒y - 2 = 5x - 10

⇒y = 5x - 8                         ...(i)

Again, 2 years later,

y + 2 = 8 + 3(x + 2)

⇒y + 2 = 8 + 3x + 6

⇒y = 3x + 12                        ...(ii)

Putting the value of y in eq.(ii) from eq.(i) :

5x - 8 = 3x + 12

⇒2x = 20

⇒x = 10

Now, putting the value of x in eq.(i) :

y = 5x - 8

⇒y = 5(10) - 8

⇒y = 50 - 8

⇒y = 42

∴ So, the present age of the man is 42 years, and the present age of his son is 10 years.

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Two years ago, a man was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The present age of the man and his son.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the present age of the man be r years

Let the present age of his son be m years

A/q

$\underbrace{\bf{2\:years\:agO\::}}}}}$

The age of the man be (r-2) years

The age of the son be (m-2) years

So;

$\longrightarrow\sf{r-2=5(m-2)}\\\\\longrightarrow\sf{r-2=5m-10}\\\\\longrightarrow\sf{r-5m=-10+2}\\\\\longrightarrow\sf{r-5m=-8}\\\\\longrightarrow\sf{r=-8+5m..........................(1)}$

$\underbrace{\bf{After\:2\:years\::}}}}}$

The age of the man be (r+2) years

The age of the son be (m+2) years

So;

$\longrightarrow\sf{r+2=8+3(m+2)}\\\\\longrightarrow\sf{r+2=8+3m+6}\\\\\longrightarrow\sf{r+2=3m+14}\\\\\longrightarrow\sf{-8+5m+2=3m+14\:\:\:\:[from(1)]}\\\\\longrightarrow\sf{5m-6=3m+14}\\\\\longrightarrow\sf{5m-3m=14+6}\\\\\longrightarrow\sf{2m=20}\\\\\longrightarrow\sf{m=\cancel{\dfrac{20}{2} }}\\\\\longrightarrow\sf{\pink{m=10\:years}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=-8+5(10)}\\\\\longrightarrow\sf{r=-8+50}\\\\\longrightarrow\sf{\pink{r=42\:years}}$

Thus;

The present age of the man is r = 42 years .

The present age of the son is m = 10 years .