Solve any three sub-questions from the following.
1) The son's age is one-third that of his father. Five years
ago father's age was 4 times as old as his son. Find their
present age.
give step by step answer
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Answers
Answer:
Given:
Son's age is ⅓ that of his father.
Five years ago, father's age was 4 times his son's age.
To Find:
What are their present ages?
Process:
To find their present ages we will first let the father's age be x. Then, son's age will be x/3. Five years ago son's age will be (x/3 - 5) and father's age will be (x - 5). It is given father's age was 4 times son's age. So, we can form an equation as follows:
x - 5 = 4(x/3 - 5)
After solving the equation to get the value of x, the value of x is equal to the age of the father and x/3 will be the age of the son.
Solution:
Let the father's age be x.
Then, the son's age will be x/3.
Five years ago:
Son's age = (x/3 - 5)
Father's age = (x - 5)
∵ Five years ago father's age was 4 times his son's age. [given]
\therefore\sf{x-5=4\bigg(\dfrac{x}{3}-5\bigg)}∴x−5=4(
3
x
−5)
\implies\sf{x-5=\dfrac{4x}{3}-20}⟹x−5=
3
4x
−20
\implies\sf{x-\dfrac{4x}{3} = 5-20}⟹x−
3
4x
=5−20
\implies\sf{\dfrac{3x-4x}{3}=-15}⟹
3
3x−4x
=−15
\implies\sf{\dfrac{-x}{3}=-15}⟹
3
−x
=−15
\implies\sf{-x=-15\times3}⟹−x=−15×3
\implies\sf{\not\!\!{-}x=\not\!\!{-}45}⟹
−x=
−45
\implies\sf{x = 45}⟹x=45
Hence, value of x is 45.
Therefore, father's age = x = 45 years
And son's age = x/3 = 45/3 = 15 years
Answer:
Given:
Son's age is ⅓ that of his father.
Five years ago, father's age was 4 times his son's age.
To Find:
What are their present ages?
Process:
To find their present ages we will first let the father's age be x. Then, son's age will be x/3. Five years ago son's age will be (x/3 - 5) and father's age will be (x - 5). It is given father's age was 4 times son's age. So, we can form an equation as follows:
x - 5 = 4(x/3 - 5)
After solving the equation to get the value of x, the value of x is equal to the age of the father and x/3 will be the age of the son.
Solution:
Let the father's age be x.
Then, the son's age will be x/3.
Five years ago:
Son's age = (x/3 - 5)
Father's age = (x - 5)
∵ Five years ago father's age was 4 times his son's age. [given]
\therefore\sf{x-5=4\bigg(\dfrac{x}{3}-5\bigg)}∴x−5=4(
3
x
−5)
\implies\sf{x-5=\dfrac{4x}{3}-20}⟹x−5=
3
4x
−20
\implies\sf{x-\dfrac{4x}{3} = 5-20}⟹x−
3
4x
=5−20
\implies\sf{\dfrac{3x-4x}{3}=-15}⟹
3
3x−4x
=−15
\implies\sf{\dfrac{-x}{3}=-15}⟹
3
−x
=−15
\implies\sf{-x=-15\times3}⟹−x=−15×3
\implies\sf{\not\!\!{-}x=\not\!\!{-}45}⟹
−x=
−45
\implies\sf{x = 45}⟹x=45
Hence, value of x is 45.
Therefore, father's age = x = 45 years
And son's age = x/3 = 45/3 = 15 years
Step-by-step explanation:
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