Question

16. A man is thrice as old as his son. Five years ago the man was four times as old as his son.
Find their present ages if man is 3x and son is x.
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Answer 1

Given :

A man is thrice as old as his son. Five years ago the man was four times as old as his son.

To FinD :

Find their present ages.

Solution :

Analysis :

Here we have to first understand the question. Making an equation on the ages of the father and the son we can find their present ages.

Explanation :

Let the son's age be "x" years.

Then, Father's age is "3x" years.

Five years ago,

• Son = (x - 5) years
• Father = (3x - 5) years

☯ According to the question,

Five years ago the man was four times as old as his son.

So,

⇒ 3x - 5 = 4(x - 5)

On expanding the brackets,

⇒ 3x - 5 = 4x - 20

Transposing 3x to RHS and 20 to LHS,

⇒ -5 + 20 = 4x - 3x

⇒ 15 = x

∴ x = 15.

Their ages :

• Son = x = 15 years
• Father = 3x = 3 × 15 = 45 years

The present age of son and father is 15 years and 45 years respectively.

Answer 2

GivEn :

• Age of man is thrice as old as his son
• Five years ago, man was four times as old as his son.

To finD :

• Present age of man and son.

Solution :

Here, we have given that man is thrice as old as his son.

So,

Let suppose that son age is x.

According to the given condition,

Age of man will be 3x

So,

• Age of son = x
• Age of man = 3x

Now,

Given that, Five years ago, man was four times as old as his son. Hence,

Age of both people before 5 years :

• Age of son before 5 years = x - 5
• Age of man before 5 years = 3x - 5

Now,

According to the given condition,

4(x - 5 ) = 3x - 5 ••••••••( 1 )

Let solving this equation :

4( x - 5 ) = 3x -5

=> 4x - 20 = 3x - 5 [ Making like terms in one side]

=> 4x - 3x = -5 + 20

=> x = 15

∴ Age of son = 15 years

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

Now, we found that age of son is 15 years.

So,

it is given that man is thrice as old as his son.

hence,

Age of man = 3 × age of son

=> Age of man = 3×15

=> Age of man is 45 years.

Hence, their present age are :-

$\large{\boxed{\bf{\green{Age~ of ~son~ = 15 years}}}}$

$\large{\boxed{\bf{\green{Age~ of~ man~ = 45 years~}}}}$