Question

Maths




Two years ago, Dilip 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.

Answer 1

Let Dilip's son's age 2 years ago be x years.

Then, Dilip's age 2 years ago = (3x) years.

.·. the son's age 2 years hence = ( x + 4 ) years.

Dilip's age 2 years hence = ( 3x + 4 ) years.

.·. 2 ( 3x + 4 ) = 5 ( x + 4 )

=> 6x + 8 = 5x + 20

=> 6x - 5x = 20 - 8

=> x = 12.

.·. Dilip's son's age 2 years ago = 12 years.

And Dilip's age 2 years ago = 3 × 12 = 36 years.

.·. son's present age = 14 years, and

Dilip's present age

=> 3x + 4

=> 3 × 12 + 4

=> 38 years.

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Now, let's check the solution :

As obtained the son's present age is 14 years and Dilip's present age is 38 years.

(i) Son's age 2 years ago

=> 14 - 2

=> 12 years.

Dilip's age 2 years ago

=> 38 - 2

=> 36 years.

.·. 2 years ago , Dilip's age= 3 × (son's age)

Thus, the first condition is verified.

(ii) Son's age 2 years hence

= 14 + 2

= 16 years.

Dilip's age 2 years hence

= 38 + 2

= 40 years.

.·. 2 years hence,

2 × (Dilip's age)= 2 × 40 = 80 years.

5 × (Son's age) = 5 × 16 = 80 years.

.·. 2 years hence,

2 × (Dilip's age) = 5 × (Son's age) .

Thus, the second condition is also verified.

________________________

Thanks for the question !

Answer 2

Let the present age of Dilip and his son be$\blue{ x }$and $\blue{ y }$ respectively.

According to question...

$\red{Two\:years\:ago}$

(x-2)=3(y-2)-----(1)

$\red{Two\:years\:Later}$

2(x+2)=5(y+2)----(2)

from equations-(1)

x=3y-4

put value of x in eq(2)

we get-

y=14
and x=38

So,
$\boxed{\blue{Age\:of\:Dilip\:is\:38years}}$

$\boxed{\orange{Age\:of\:Dilip's \:son\:is\:14\:years}}$