Question

Five years ago, father's age was 5 times that of his son and after 3 years he will be 3 times as old as his son. Find the present age of son ?
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Answer 1

Answer:

A father is 5 times as old as his son, and he will be 3 times as old as his child in 5 years. What are their present ages?

Power to create from anywhere.

Let son's present age be x,

As per statement father is 5 times as old as his son, therefore father's age is 5x.

In five years their ages will be son x + 5 and father 5x + 5.

The father will be 3 times as old as his child in 5 years.

5x + 5 =3 (x + 5)

5x + 5 = 3x + 15

5x - 3x =15 -5

2x = 10

x = 10/2

x = 5

Son's age is 5 years.

Father's age is 5x. Means 5 × 5=25 years

Answer son's age 5 years and father's age 25 years

Answer 2

Given:-

• Five years ago, father's age was 5 times that of his son.
• After 3 years, Father will be 3 times as old as his son.

To Find:-

• What is the present age of son ?

Solution:-

Let the present age of father be 'x' and the present age of son be 'y'

✫ Five years ago, father's age was 5 times that of his son.

• Father's age = (x – 5) years
• Son's age = (y – 5) years

${\underline{\bf{According \: To \: Question:-}}}$

$\sf{\longmapsto (x -5) = 5(y-5) }$

$\sf{\longmapsto x-5 = 5y -25}$

$\sf{\longmapsto x -5y = -25+5 }$

$\sf{\longmapsto x - 5y = -20 }$

$\sf{\longmapsto x = 5y -20...1)}$

Now,

✫ After 3 years, Father will be 3 times as old as his son.

• Father's age = (x+3) years
• Son's age = (y +3) years

${\underline{\bf{According \: To \: Question:-}}}$

$\sf{\longmapsto (x +3) = 3(y+3)}$

$\sf{\longmapsto x +3 = 3y +9 }$

$\sf{\longmapsto x -3y = 9-3 }$

$\sf{\longmapsto x - 3y = 6....2)}$

Put the value of 'x' in equation 2) from equation 1)

$\sf{\longmapsto 5y -20 -3y = 6 }$

$\sf{\longmapsto 2y = 6+20}$

$\sf{\longmapsto 2y = 26 }$

$\sf{\longmapsto y = \cancel\dfrac{26}{2}}$

${\large{\underbrace{\bf{\star \: y = 13 \: \star }}}}$

On putting the value of 'y' in equation 1), we get

$\sf{\longmapsto x = 5 \times 13 - 20 }$

$\sf{\longmapsto x = 65 -20}$

${\large{\underbrace{\bf{\star \: x = 45 \: \star }}}}$

✧ Father's age = x = 45 years

✧ Son's age = y = 13 years

Hence, the father's age is 45 years and Son's age is 13 years

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