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Answer 1

Appropriate Question:

• Five years hence,father's age will be three times the age of his son.Five years ago,father was seven times as old as his son.Find their present ages.

Given in the Question: We are provided with five years later,father's age will be three times the age of his son.Five years ago,father was seven times as old as his son.

Need to Find: Their present ages?

$\quad\quad\quad$_______________

❍Let's say that,the present age of father be x years and present age of son be y years.

$\large{\bigstar{\mathfrak{\underline{According\:to\:the\:Question}}}}$

• In the first condition,five years later,father's age will be three times the age of his son.So,let's solve -

Therefore,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: x + 5 = 3(y + 5) \\ \\ \: \: \: \: \sf \implies \: x + 5 = 3y + 15$

$\sf\implies{x = 3y + 10}$$\:\:\:$${\Big[}{eq.1}{\Big]}$

• In the second condition,five years ago,father was seven times as old as his son.So,let's solve -

Therefore,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: x - 5 = 7(y - 5) \\ \\ \: \: \: \: \: \: \sf \implies \: x - 5 = 7y - 35$

$\sf\implies{x - 7y = -30}$$\:\:\:$${\Big[}{eq.2}{\Big]}$

$\large{\bigstar{\mathfrak{\underline{Substitute\:the\:values}}}}$

Put the value of x from eq 1 : -

$\: \: \: \: \: \: \: \: \: \sf \implies \: 3y + 10 - 7y= - 30 \\ \\ \: \: \: \: \: \: \sf \implies \: - 4y = - 40 \\ \\ \: \: \: \: \: \: \sf \: y = \cancel \frac{ - 40}{ - 4}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:$$\sf\implies{\boxed{\underline{\purple{ y = 10}}}}$

Put y = 10 in eq 1

$\: \: \: \: \: \: \: \sf \implies \: x = 3 \times 10 + 10 \\ \\ \: \: \: \: \: \: \: \: \: \sf \implies \: x = 30 + 10$

$\:\:\:\:\:\:\:\:\:\:\:$$\sf\implies{\boxed{\underline{\purple{ x = 40}}}}$

Hence,

• Present age of Father = 40 years

• Present age of Son = 10 years

______________________

Answer 2

Answer:

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