Question

A person’s present age is two­fifth of the age of his mother. After 8 years, he will be half of the age of his mother. How old is the mother at present?​

Answer 1

Answer:

⇢ ${\boxed{\bold{Present \: age \: of \: mother = 40 \: years}}}$

Step-by-step explanation:

Given:-

⇢ A person’s present age is two­fifth of the age of his mother. After 8 years, he will be half of the age of his mother.

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Find:-

⇢ How old is the mother at present?

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Calculations:-

• Let x be the present age of mother and 2/5x be the present age of person.

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After eight years ages:

⇢ $\rm{Mother = x + 8}$

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⇢ $\rm{Person = \dfrac{2}{5x} + 8}$

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Finding the preson age of mother:-

⇢ $\rm{\dfrac{2}{5x + 8} = \dfrac{1}{2} (x + 8)}$

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⇢ $\rm{40 + \dfrac{2x}{5} = \dfrac{x}{2+4}}$

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⇢ $\rm{\dfrac{40 + 2x = 5}{2x + 20}}$

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⇢ $\rm{40 - 20 = (\dfrac{5}{2 - 2})x}$

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⇢ $\rm{20 = \dfrac{1}{2x}}$

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⇢ ${\boxed{\bold{x = 40}}}$

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Therefore, 40 is the present age of mother.

Answer 2

EXPLANATION.

A person present age is 2/5 th of the age of

his mother.

after 8 years,he will be half of the age of his

mother.

How old is the mother at present.

According to the question,

Let the present age of person be = x years.

Let the present age of mother be = y years.

Case = 1

A person present age is 2/5 th of the age of

his mother.

=> x / y = 2/5

=> 5x - 2y = 0 .....(1)

Case = 2

after 8 years,he will be half of the age of his

mother.

=> x + 8 = 1/2 ( y + 8 )

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

=> 2x + 16 = y + 8

=> 2x - y = -8 .....(2)

From equation (1) and (2) we get,

=> 5x - 2y = 0

=> 4x - 2y = -16

we get,

=> x = 16

put x = 16 in equation (1)

=> 5(16) - 2y = 0

=> 80 - 2y = 0

=> y = 40

Therefore,

Present mother age = 40 years.