Question

Question:-

Two years ago. Dllip 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. Check your solution

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Answer 1

solution:-

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 )

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

∴ 2 ( 3x +4 ) = 5 ( x+ 4)

➡ 6x +8 = 5x +20

➡ x = 12.

∴ Dilip's son's age 2 years ago = 12 years

and Dilip's age 2 years ago = 36 years.

∴ son's present age = 14 years, and

Dilip's present age = 38 years.

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

(1) son's age 2 years ago = ( 14 -2 ) years = 12 years.

Dilip's age 2 years ago = ( 14-2 )years = 12 years.

∴ 2 year's ago, Dilip's age = 3 × ( son's age).

Thus , the first condition is verified.

(2) Son's age 2 years hence = ( 14 +2 ) years =16 years

Dilip's age 2 years hence = ( 38 + 2 ) years= 40 years

∴ 2 years hence ,

2 × ( Dilip's age ) = ( 2×40 years) = 80 years, and

5 × ( son' age ) = ( 5× 16 ) years = 80 years

∴ 2 years hence , 2 × ( Dilip's age) = 5× ( son's age) .

Thus , the second condition is also verified.

Answer 2

Given :

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.

To find :

Find their present ages.

Solution :

Let the present age of Dilip be 'a' years and age of his son be 'b' years.

According to 1st condition :

⇒ a - 2 = 3(b - 2)

⇒ a - 2 = 3b - 6

⇒ a = 3b - 6 + 2

⇒ a = 3b - 4               _(1)

Now 2nd condition :

⇒ 2(a + 2) = 5(b + 2)

⇒ 2a + 4 = 5b + 10

⇒ 2a = 5b + 10 - 4

⇒ 2a = 5b + 6

⇒ 2(3b - 4) = 5b + 6 [Putting value from (1)]

⇒ 6b - 8 = 5b + 6

⇒ 6b - 5b = 6 + 8

⇒ b = 14 years

∴ Present age of his son = 14 years.

Now putting value of b in (1) :

⇒ a = 3(14) - 4

⇒ a = 42 - 4

⇒ a = 38 years

∴ Present age of Dilip = 38 years.

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Verification :

Putting value of a and b in 1st condition :

⇒ a - 2 = 3(b - 2)

⇒ 38 - 2 = 3(14 - 2)

⇒ 36 = 3 × 12

⇒ 36 = 36

∴ 1st condition is verified.

Now putting value of a and b in 2nd condition :

⇒ 2(a + 2) = 5(b + 2)

⇒ 2(38 + 2) = 5(14 + 2)

⇒ 2 × 40 = 5 × 16

⇒ 80 = 80

∴ 2nd condition is also verified.

Therefore,

Present age of Dilip is 38 years and present age of his son is 14 years.