Question

Q5: The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be: [UPSC 2003]

A) 12 years B) 14 years C) 18 years D) 20 years

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Answer 1

QUESTION:-

The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be: [UPSC 2003]

A) 12 years B) 14 years C) 18 years D) 20 years

EXPLANATION:-

Let the present age of son be "x" years

then his fathers present age "(60-x)" years

Now ,

A.TQ.

(60−x)−6=5(x−6)

 54−x=5x−30

 54+30=5x+x

84=6x

x=84/6

x=14

So son's present age=14 yeas

his age after 6 years=14+6

=>20 years

So ,

opt-[D] is the required answer

Answer 2

Question:

• The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be ?

Answer:

• The age of the son after 6 years will be 14 years

Step-by-step Explanation:

Given that:

• The sum of the present ages of a father and his son is 60 years
• Six years ago, father’s age was five times the age of the son.

To Find:

• The son's age after the time period of 6 years will be

Assumptions Made:

• Let the present age of son be $\pink{ \bf {x}}$
• Let the present age of father be $\blue{\bf{ 60 - x }}$

According to the Question:

• Six years ago, father’s age was five times the age of the son

➻ 60 - x - 6 = 5 ( x - 6 )

➻  60 - x - 6 = 5x - 30

➻  54 - x = 5x - 30

➻  5x + x = 54 + 30

➻  6x = 84

• Solving the linear equation further

➻ $\bf 6x = 84$

➻ $\bf x = \cancel\dfrac{84}{6}$

➻ ${\red{\bf{ x = 14 }}}$

∴ The present age of the son will be 14 years

The son's age after 6 years will be:

→ The son's age after 6 years will be = x + 6 years

→ The son's age after 6 years will be = 14 + 6 years

→ The son's age after 6 years will be = ${\purple{\bf{ 20 \; years }}}$

Therefore:

• The son's age after 6 years will be 20 years

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