Question

$\underline{\underline{\huge{\textsf{Solution:}}}}$

Two years ago , father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son . Find their present ages ..
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Answer 1

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.

Answer 2

Given :-

• Two years ago , father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son.

Need To Find out :-

• Present Age of Father = ?
• Present Age of Son = ?

Solution :-

Let the present age of the son be x years. (2 years ago). Then the age of his father will be 3x.

Now according to the question , we need to find the the present ages of the father & his son.

${\underline{\pmb{\frak{\bigstar\green{ \: Present \: Ages}}}}}$

• Age of father = 3x +2
• Age of his son = x + 2

${\underline{\pmb{\frak{\bigstar\green{ \: After \: 2 \: years }}}}}$

• Age of father = 3x + 2 +2 = x+4
• Age of son = x +2+2 = x+4

According to the question :-

$\sf \leadsto 2(3x+4) = 5 \times (x+4)$

$\sf \leadsto 6x+8 = 5x+20$

$\sf \leadsto 6x-5x = 20 - 8$

$\leadsto\underline{\boxed{\frak{\pmb{\red{x = 12}}}}}\:\bigstar$

Hence,

• Present age of father = 3×12 + 2= 38 years
• Present age of son = 12 +2 = 14 years