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 :

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

$\rule{300px}{.3ex}$

❍ 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

Answer:

This is your answer

Step-by-step explanation:

Answer:

Let us consider

Son’s age = X

Two years ago son’s age = X – 2

His Father’s age at that time = 3(X – 2)

Present age of Father = 3X – 6 + 2

The present age of Father = 3X – 4

Two years hence father’s age = 3X – 4 + 2

Two years hence father’s age = 3X – 2

Two years hence son’s age = X + 2

Given:

5 × (X + 2) = 2 × (3X – 2)

5X + 10 = 6X – 4

X = 14

Son’s present age X = 14 years.

Father’s present age = (3 × 14) – 4

Father’s present age = 38 years.