Question

Six years hence, a father's age will be twice the age of his son. Eightyears ago, the father was four times
as old as his son. Find their present ages.

Answer 1

Let the present age of father be F years and the age of his son be S years.

Six years hence, a father's age will be twice the age of his son.

Six years hence, age of father = (F + 6) years

Age of son = (S + 6) years

According to question,

Six years hence, the age of father = 2(Six years hence, the age of his son)

⇒ F + 6 = 2(S + 6)

⇒ F + 6 = 2S + 12

⇒ F = 2S + 12 - 6

⇒ F = 2S + 6

Eight years ago, the father was four times

as old as his son.

Eight years ago, the age of father = (F - 8) years

And age of his son = (S - 8) years

According to question,

⇒ F - 8 = 4(S - 8)

⇒ F - 8 = 4S - 32

⇒ F = 4S - 24

On comparing we get,

⇒ 4S - 24 = 2S + 6

⇒ 4S - 2S = 6 + 24

⇒ 2S = 30

⇒ S= 15

Substitute value of S in F

⇒ F = 2(15) + 6

⇒ F = 30 + 6

⇒ F = 36

Therefore, the present age of the father is 36 years and son is 15 years.

Answer 2

Solution ⓵ :-

Basic Method .

Let Present age of son = x years.

Let Present Age of Father = y years.

So,

→ After 6 Years son will be = (x + 6) years old .

→ After 6 Years Father will be = (y + 6) years old .

A/q,

→ Father = 2 * son

→ (y + 6) = 2(x + 6)

→ y + 6 = 2x + 12

→ y - 2x = 12 - 6

→ y - 2x = 6 -------------------------- Equation ❶

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Now, it is Also given That, Eight years ago, the father was four times as old as his son.

So,

→ Before 8 Years son was = (x - 8) years old .

→ Before 8 Years Father was = (y - 8) years old .

A/q,

→ Father = 4 * son

→ (y - 8) = 4 (x - 8)

→ y - 8 = 4x - 32

→ 4x - y = - 8 + 32

→ 4x - y = 24 -------------------------- Equation ❷

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Adding Equation ❶ & Equation ❷ Now, we get,

→ (4x - y) + (y - 2x) = 24 + 6

→ 4x - 2x - y + y = 30

→ 2x = 30

→ x = 15 years.

Putting value of X in Equation ❶ now, we get ,

→ y - 2*15 = 6

→ y = 6 + 30

→ y = 36 years.

Hence, we can say That, Present age of son is 15 Years and His Father is 36 Years.

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Solution ⓶ :-

Ratio Method .

Shortcut Trick to Solve Question :

⋆ Present Age⠀⠀➞ 6 Yrs.⠀⋆ Future Age

Son ⠀⠀⠀ : Father

⠀⠀1⠀⠀⠀⠀⠀ ⠀:⠀⠀ 2⠀⠀⠀⠀⠀⠀

⋆ Present Age⠀⠀➞ 8 Yrs.⠀⋆ Ago Age

Son ⠀⠀⠀ : Father

⠀ ⠀1⠀⠀⠀⠀⠀ ⠀:⠀⠀ 4⠀⠀

◗ Difference of both Ratios is :-

(2 - 1) = 1 and, (4 - 1) = 3, we will Multiply them by Opposite terms. Means by 3 in Future and By 1 in Past to make Difference Equal.

⠀⠀1 : 2⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀1 : 4

× 3 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀× 1

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⠀⠀3 : 6⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀1 : 4

Now, Difference Between Ratios are Same, i.e. (3 - 1) = (6 - 4) = 2.

So, we will find the Difference of Ratio in Ages, that Means we can find from like Son (3 - 1) = 2 or, Father (6 - 4) = 2.

Now, Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ (6+8) / 2

↦ 7

Now, Just Multiply the Outcome with any of the Ratio of find Age. Here we have to Find Future or Past Age :

◗ Son = (3 × 7) = 21 Years = 6 Year Hence.

◗ Father = (6 × 7) = 42 Years = 6 Year Hence.

Hence,

☛ son Present Age = 21 - 6 = 15 Years.

☛ Father Present Age = 42 - 6 = 36 Years.

∴ Therefore, Present Age of Son is 15 Years and Present Age of Father is 36 Years.

Think Smart , Work Smart.

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