Question

ten years ago father was 3 times old as his son and 2 years hence, twice his age will be equal to five times that of his son. Find their present ages​

Answer 1

Answer:

Sry may be have written ten years ago or I am wrong.....And if I am not wrong then in the starting of the question it shoulb be two years ago...

Step-by-step explanation:

And If I Am Write Then The Answer Is !!

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.

Hope It will help you....Marks me as the BRAINLIST

Answer 2

$\blue\bigstar$Answer:

• Present age of son = 46 years
• Present age of his father = 118 years

$\pink\bigstar$Given:

• Ten years ago, father was 3 times old as his own.
• 2 years hence, twice his age will be equal to five times that of his son.

$\red\bigstar$To find:

• The present ages of both father and son.

$\blue\bigstar$ Solution:

Let's assume the age of son be x.

Two years ago, age of son

= Present age - 10

= $\boxed{x \:- 10\:}$

At that time, the age of his father

= 3 (Age of his son)

= 3 (x - 10)

= $\boxed{3x \:- 30\:}$

The Present age of his Father

= 3x - 30 + 10

= $\boxed{3x \:- 20\:}$

Two years hence, father’s age

= 3x - 20 + 2

= $\boxed{3x\: - \:18}$

Two years hence, age of the son

= $\boxed{x\: + 2\:}$

Now after 2 years,

$\hookrightarrow$ 2 (Father's Age) = 5 (Son's Age)

[Given]

$\implies$ 2( 3x - 18 ) = 5( x + 2 )

$\implies$ 6x - 36 = 5x + 10

[By opening the brackets]

$\implies$ 6x - 5x = 36 + 10

[Transposition Method]

$\implies$ $\boxed{x\: = \:46\:}$

$\therefore$the present age of son = $\boxed{\sf{46 \: years}}$

So, Present age of Father

= 3x - 20

= 3(46) - 20

= $\boxed{\sf{118 \: years}}$

$\pink\bigstar$ Verification:

The present age of Father = 118 years

The present age of Son = 46 years

10 years ago, father was 3 times as old his son was.

Age of son 10 years ago

= 46 years - 10 years

= 36 years

Age of Father 10 years ago,

= 118 years - 10 years

= 108 years

= 3 ( 36 years )

= 3 ( Son's Age )

$\green\bigstar$Hence Verified too.

$\red\bigstar$ Concepts Used:

• Assumption of ages in terms of x
• Forming Expressions and equating them.
• Solving the equation
• Opening of Brackets
• Transposition Method