Question

two years ago dilip was three times as old is his son and two years hence twice his age will be equal to five times that of his son ,find their present ages?​

Answer 1

A N S W E R :

$\large{\underline{\boxed{\frak{ Ages = 14 \; years \;\&\; 38 \: years}}}}$

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

But, Two years ago —

• Dilip's age = (x – 2) years
• Son's age = (y – 2) years

$\underline{\bigstar\:\pmb{\frak{ According\; to \;the\; given \;Question :}}}$

• Two years ago Dilip was three times as old as his son.

➟ Dilip's age = 3(Son's age)

➟ (x – 2) = 3(y – 2)

➟ x – 2 = 3y – 6

➟ x = 3y – 4 ⠀⠀⠀⠀⠀⠀—eq.( I )

⠀⠀⠀⠀

• And, two years hence twice his age (dilip's age) will be equal to five times that of his son.

Therefore,

$:\implies\sf 2(x + 2) = 5(y + 2) \\\\\\:\implies\sf 2x + 4 = 5y + 10 \\\\\\:\implies\sf 2(3y - 4) + 4 = 5y + 10\\\\\\:\implies\sf 6y - 8 = 5y + 6\\\\\\:\implies\sf 6y - 5y = 8 + 6\\\\\\:\implies\underline{\boxed{\frak{\pink{y = 14}}}}\:\bigstar$

⠀⠀⠀

⠀⠀$\underline{\bf{\dag} \:\mathfrak{Putting\;the\;value\;of\;y\;in\;eq^n \;(1)\: :}}$⠀⠀⠀⠀

⠀⠀⠀

$:\implies\sf x = 3y - 4 \\\\\\:\implies\sf x = 3(14)-4 \\\\\\:\implies\sf x = 42 - 4 \\\\\\:\implies\underline{\boxed{\frak{\purple{x = 38}}}}\:\bigstar$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

⠀

Hence, their ages are —

• Present age of Dilip, x = 38 years
• Present age of Dilip's son, y = 14 years

$\therefore{\underline{\textsf{Hence, their present ages are \textbf{38 years} \sf{and} \textbf{14 years} respectively.}}}$⠀⠀⠀⠀

Answer 2

Given :-

Two  years ago dilip was three times as old is his son and two years hence twice his age

To Find :-

Present ages

Solution :-

Let the son age be x

Age of father = 3x

Two years ago

Age of son = x - 2

Age of father = 3(x - 2)

Now

After 2 years

Age of son = x + 2

Age of father = 3(x - 2) + 2 = 3x - 6 + 2 = 3x - 4

ATQ

$\sf 5(x+2) = 2(3x - 2)$

$\sf 5x + 10=6x-4$

$\sf 6x - 5x = 10 + 4$

$\sf x=14$

Age of son = 14 years

Age of father = 3(14) - 4 = 42 - 4 = 38 years