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:

Let us consider

Let us considerSon’s age = X

Let us considerSon’s age = XTwo years ago son’s age = X – 2

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:5 × (X + 2) = 2 × (3X – 2)

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:5 × (X + 2) = 2 × (3X – 2)5X + 10 = 6X – 4

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:5 × (X + 2) = 2 × (3X – 2)5X + 10 = 6X – 4X = 14

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:5 × (X + 2) = 2 × (3X – 2)5X + 10 = 6X – 4X = 14Son’s present age X = 14 years.

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:5 × (X + 2) = 2 × (3X – 2)5X + 10 = 6X – 4X = 14Son’s present age X = 14 years.Father’s present age = (3 × 14) – 4

Let us considerSon’s age = XTwo years ago son’s age = X – 2His Father’s age at that time = 3(X – 2)Present age of Father = 3X – 6 + 2The present age of Father = 3X – 4Two years hence father’s age = 3X – 4 + 2Two years hence father’s age = 3X – 2Two years hence son’s age = X + 2Given:5 × (X + 2) = 2 × (3X – 2)5X + 10 = 6X – 4X = 14Son’s present age X = 14 years.Father’s present age = (3 × 14) – 4Father’s present age = 38 years.