Question

   A man is five times old as his son. After 14 years he will be only thrice as old as his son. Find their present ages.
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Answer 1

Given -

•  A man is five times old as his son. After 14 years he will be only thrice as old as his son.

To find -

• Their present ages.

Solution -

Let the common ratio be termed as x

Son's age = x

man's age = 5x

After 14 yrs -

Son's age = x + 14

Man's age = 5x + 14

So,

now, we will make a linear equation, and then we will equate the whole expression.

On substituting the values -

$\longrightarrow$ 5x + 14 = 3(x + 14)

$\longrightarrow$ 5x + 14 = 3x + 42

$\longrightarrow$ 5x - 3x = 42 - 14

$\longrightarrow$ 2x = 28

$\longrightarrow$ x = $\sf\cancel\dfrac{28}{2}$

$\longrightarrow$ x = 14

Now -

Son's age = 14yrs

Man's age = 5 × 14 = 70yrs

$\therefore$ The present ages of man and son is 14yrs and 70yrs

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Answer 2

Answer:

Question

A man is five times old as his son. After 14 years he will be only thrice as old as his son. Find their present ages.

Step-by-step explanation:

Given in the question:-

• A man is five times old as his son
• After, 14 yrs he will be be only thrice as old as his son .

To find out in the question:-

◇ To find out there present ages

Now,

Let

• The son's age be X
• And, his father's age be 5x

After 14 yrs passed,

Son's age will increase by 14 from present age i.e. the equation becomes

$son \: age \: is \: (x + 14) \: yrs$

Now, father's age will increase by 14 from present age i.e. the equation becomes

$father \: age \: is \: (5x + 14)yrs$

Now, Let's solve it through linear equations

Let's solve your equation step-by-step

Substituting the values let's find out:-

$= > 5x + 14 = 3(x + 14)$

$= > 5x + 14 = 3x + 42$

$= > 5 - 3x = 42 - 14$

$= > 2x = 28$

$= > x = \frac{28}{2}$

So, 28 when divided by 2 it comes 14

$now \: calculating \: their \: present \: ages$

$son \: present \: age \: is \: = x \: and \: we \: got \: the \: x \: value \: as \: 14 \: so \: equation \: becomes \: in \: this \: type$

$son \: age \: = \: x \: = 14$

$•°•sons \: age \: is \: 14 \: yrs$

$father\: age \: is \: 5x + 14 \\ \: so \: putting \: x \: value \: lets \: find \: out$

$5 \times 14 = 70 \: yrs$

$•°•fathers \: age \: becomes \: 70 \: yrs$

So, present age of father 70 yrs and present age of child is 14 yrs

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