Question

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

Answer 1

Given :-

• Two years ago  ,Dilip was three times as old as his son
• wo years hence , twice his age will be equal to five times that of his son

To Find :-

• Their Present ages

Solution :-

→ Let the present age of

   Dilip be ' x '

   His son be ' y '

→ Then , two years before their ages can be written as

 Dilip = ( x - 2 )

 His Son = ( y - 2 )

→ ATQ  we can form a equation

➝ ( x - 2 ) = 3( y - 2 )

➝  x - 2 = 3y - 6

( keeping variable one side and constant other side )

➝ x - 3y = - 2 + 6

( we can write it as )

➝ x - 3y - 2 + 6 = 0  

➝ 2x = 6y - 8 ( i )

→ Now , considering their age after two years

 Dilip = ( x + 2 )

 Son = ( y + 2 )

→ Now , ATQ  we can again form an equation

➝ 2( x + 2 ) = 5 ( y + 2 )

➝ 2x + 4 = 5y +10

➝ 2x  -5y = 10 - 4

➝ 2x - 5y = 6  

➝ 2x = 5y + 6  -- ( ii )

→ Now let's equate equations ( i ) and ( ii ) .

  There , 2x will cancel

➝ 6y − 8 = 5y + 6

➝ y = 6 + 8

➝ y  = 14

→ As we've got the value of y  , can find the value of ' x ' by substituting the values in equation ( i )

➝ x = 3y − 4

➝ x  = ( 3 × 14 ) − 4

➝ x = 42 − 4

➝ x = 38

∴ Age of Dilip ' x ' is 38 years

  Age of Son ' y ' is 14 years

Answer 2

$\huge{\rm{Required \ Answer :)}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

Dilip's age 2 years ago = 3 × Age of his son

Dilip's present age = (3 × Age of his son) + 2

$\sf{\bold{\red{\underline{\underline{To~find}}}}}$

Present age of Dilip.

Present age of his son.

$\sf{\bold{\orange{\underline{\underline{Solution}}}}}$

Let the age of son 2 years ago be x and then, Dilip's age would be 3x

Assume that,

• x = Age of son after 2 years
• 3x = Age of Dilip after 2 years
• x + 2 = Present age of son
• 3x + 2 = Present age of Dilip

After two years,

Son's age = $\sf x+2+2 =x+4$

Dilip's age = $\sf 3x+2+2=3x+4$

According to the question,

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

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

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

$\sf -x=-12$

$\sf x=12$

$\boxed {\sf {\blue{ Hence,~the~value~of~x~is~ 12}}}$

Finding their present ages,

Present age of his son = $\sf x+2=12+2=14$

Present age of son = 14 years

Present age of Dilip = $\sf 3x+2=( 3\times 12)+2$

Present age of Dilip = $\sf 36+2=38$ years

Therefore, the present ages of Dilip and his son are 38 years and 14 years respectively.