Question

A man is 5 times as old as his son .he will be three times as old a his after 10 years .find their present ages
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Answer 1

Solution :-

Let :-

Present age of son = x

Present age of man = y

After 10 years :-

Age of son = x + 10

Age of man = y + 10

According to the first condition :-

$\longrightarrow \sf y = 5x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition :-

$\longrightarrow \sf 3(x+10) = y +10 \\\\\longrightarrow 3x+30 = y+10 \\\\\longrightarrow 3x-y = 10-30 \\\\\longrightarrow 3x-y = -20 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf 3x - 5x = -20 \\\\\longrightarrow -2x = -20 \\\\\longrightarrow \bf x = 10$

Substitute x = 10 in eq (1) :-

$\longrightarrow \sf y = 5 \times 10 \\\\\longrightarrow \bf y = 50$

Present age of son = 10 years

Present age of man = 50 years

Answer 2

Given:-

• At present a man is 5times as old as his son.
• After 10yrs he will be three times as old as his son.

Find:-

• Their present ages.

Solution:-

Let, Age of a man's be 'x' yrs

and age of his son's be 'y' yrs

⛇$\large{\red{\textsf{According To Question:-}}}$

A men is 5times the age of his son.

$\sf \implies x = 5y \qquad \bigg \lgroup Equation \: 1 \bigg \rgroup$

Now, After 10yrs His age will be three times the age of his son.

$\sf \implies x + 10= 3(y + 10) \qquad \bigg \lgroup Equation \: 1 \bigg \rgroup$

✯$\underline{\sf Substituting\:eq.1\:in\:eq.2}$

$\sf \dashrightarrow x + 10= 3(y + 10)$

$\sf \dashrightarrow (5y) + 10= 3(y + 10)$

$\sf \dashrightarrow 5y + 10= 3y + 30$

$\sf \dashrightarrow 5y - 3y= 30 - 10$

$\sf \dashrightarrow 2y= 20$

$\sf \dashrightarrow y= \dfrac{20}{2}$

$\sf \dashrightarrow y= 10yrs$

◕$\underline{\sf Substituting\:value\:of\:y\:in\:eq.1}$

$\sf :\implies x = 5y$

$\sf :\implies x = 5(10)$

$\sf :\implies x = 50yrs$

____________________________

$\underline{\boxed{\therefore \textsf{Age of a man, x = 50yrs}}}$

$\underline{\boxed{\therefore \textsf{Age of his son, y = 10yrs}}}$