Question

A son's present age is half the present age of his mother. Ten years ago, the mother was thrice as old as her son. What are their present ages?

$\rm Please \: help \: me!!!$
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Answer 1

Answer:

Let the present age of the mother be x years

As the son's age is half the present age of his mother, therefore,

the present age of the son = 1/2x years

Ten years ago,

the age of the mother = (x-10) years

and the age of the son = (1/2x - 10) years

According to the problem ,

x - 10 = 3(1/2x - 10)

=> x - 10 = 3/2x - 30

=> 2x - 20 = 3x - 60 (multiplying both sides by 2)

=> 2x - 3x = 60+20

=> -x = -40

=> x = 40

Therefore , the present age of the mother = 40 years

and the present age of the son = 1/2 × 40

= 20 years

Step-by-step explanation:

Answer 2

Answer :-

• The son's present age is 20 years
• The mother's present age is 40 years.

Given :-

• A son's present age is half the present age of his mother.

• Ten years ago, the mother was thrice as old as her son.

To find :-

• Their present ages.

Step-by-step explanation :-

• Let the present age of the son be "x".

• As the son's age is half the present age of his mother, therefore,

$\longmapsto\sf The \: son's \: present \: age = \dfrac{1}{2} x$

Ten years ago,

The age of the mother was x - 10.

The age of the son was :-

$\longmapsto\sf\dfrac{1}{2} x - 10$

It has been given that :-

• Ten years ago, the mother was thrice as old as her son.

Hence,

$\rm x - 10 = 3 \bigg(\dfrac{1}{2} x - 10 \bigg)$

Multiplying 1/2x and 10 with 3,

$\rm x - 10 = \dfrac{3}{2} x - 30$

Multiplying both the sides with 2,

$\rm2x - 20 = 3x - 60$

Putting the constant and variable terms on different sides by the method of transposition,

$\rm2x - 3x = - 60 + 20$

On simplifying,

$\rm - x = - 40$

Cutting off the negative sign,

$\overline{\boxed{\rm x = 40}}$

• The value of x is 40.

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Therefore,

$\bf The \:mother's \:age = x = 40.$

$\bf The \: son's \: age = \bf \bigg( \dfrac{1}{2} \times 40 \bigg) = 20.$