Question

1- A father is 7 time as old as his son. Two years ago, the father was 13 times as old as his son. How
old are they now?​

Answer 1

❍ Let the present age of the son be x years and according to given condition the age of father be 7x years respectively.

⠀

$\underline{\bigstar\:\boldsymbol{According\;to\; the\; Question \; :}}$⠀⠀

⠀

• Two years ago, the father was 13 times as old as his son.

⠀

Therefore,

⠀

$:\implies\sf 13(x - 2) = 7x - 2 \\\\\\:\implies\sf 13x - 26 = 7x - 2 \\\\\\:\implies\sf 13x - 7x = 26 - 2\\\\\\:\implies\sf 6x = 24 \\\\\\:\implies\sf x = \cancel\dfrac{24}{6}\\\\\\:\implies \underline{\boxed{\textsf{\textbf{x = 4}}}}\;\bigstar$

⠀

Hence,

⠀

• Present age of son, x = 4 years.
• Present age of father be 7x = 7(4) = 28 years.

⠀

$\therefore{\underline{\sf{Hence, \;son\; and \; his \; father's\; present \; ages \; are\; \bf{ 4\; years \;\&\;28 years}.}}}$

Answer 2

Answer:

Given :-

• A father is 7 times as old as his son. Two years ago the father was 13 times as old as his son.

To Find :-

• What is the present age of son and father.

Solution :-

Let, the present age of son be x years

And, the present age of father will be 7x years

$\leadsto$ Two years ago,

Age of son is x - 2

And, the age of father is 7x - 2

$\sf\boxed{\bold{\green{According\: to\: the\: question :-}}}$

↦ $\sf 13(x - 2) =\: 7x - 2$

↦ $\sf 13x - 26 =\: 7x - 2$

↦ $\sf 13x - 7x =\: - 2 + 26$

↦ $\sf 6x =\: 24$

↦ $\sf x =\: \dfrac{\cancel{24}}{\cancel{6}}$

➠ $\sf\bold{\pink{x =\: 4\: years}}$

Hence, the required ages are,

$\mapsto$ Present age of son :

⇒ $\sf x\: years$

➦ $\sf\bold{\red{4\: years}}$

$\mapsto$ Present age of father :

⇒ $\sf 7x\: years$

⇒ $\sf 7(4)\: years$

⇒ $\sf 7 \times 4\: years$

➦ $\sf\bold{\red{28\: years}}$

$\therefore$ The present age of son is 4 years and the present age of father is 28 years.