Seven years back the age of a father was 5 times the age of his son. It will be twice after 14 years. Find their present age.

f-7 = 5(s-7)

f+14 = 2(s+14)
father = 42
son = 14
check:
42-7 = 35 = 5(14-7) ✅
42+14 = 56 = 2(14+14) ✅

Ah, the age-old question of ages! Let's solve this riddle with a touch of mirth.

Let's say the son's current age is S, and the father's current age is F.

Seven years ago, we can assume that the father's age was F-7, and the son's age was S-7. According to the given information, the father's age was 5 times the son's age back then.

So we can form the equation: F-7 = 5(S-7)

Now, fast forward to 14 years from now. Taking into consideration the future, we can assume that the father's age will be F+14, and the son's age will be S+14. According to the riddle, the father's age will be twice that of the son's age.

So the second equation is: F+14 = 2(S+14)

Now we need to solve these equations simultaneously to find their present ages. Shall we juggle these numbers together and find the solution?

Applying mathematical magic, we find that the son's present age (S) is 21, and the father's present age (F) is 63.

Remember, though, these numbers are no laughing matter—they're just the answers to the riddle!

Let's start by assigning variables to the present ages of the father and son. Let's say the father's present age is "F" and the son's present age is "S".

According to the given information:

"Seven years back, the age of the father was 5 times the age of his son."

This can be written as:
F - 7 = 5(S - 7) -- Equation 1

"It will be twice after 14 years."

This can be written as:
F + 14 = 2(S + 14) -- Equation 2

We now have two equations with two variables. We can solve them simultaneously to find the values of F and S.

Using Equation 1, let's simplify:

F - 7 = 5S - 35
F = 5S - 35 + 7
F = 5S - 28 -- Equation 3

Now, substitute Equation 3 into Equation 2:

5S - 28 + 14 = 2(S + 14)
5S - 14 = 2S + 28
5S - 2S = 28 + 14
3S = 42
S = 42 / 3
S = 14

Substitute the value of S back into Equation 3 to find F:

F = 5S - 28
F = 5(14) - 28
F = 70 - 28
F = 42

Therefore, the present age of the father (F) is 42 years and the present age of the son (S) is 14 years.

To find their present ages, let's assign variables:

Let "F" represent the father's current age,
Let "S" represent the son's current age.

Given information:
1. Seven years back, the father's age was 5 times the age of his son, so we can write the equation: (F - 7) = 5(S - 7).
2. In 14 years, the father's age will be twice that of his son's age, so we can write the equation: (F + 14) = 2(S + 14).

We have two equations with two variables, so we can solve them simultaneously.

First, let's solve the first equation for F:
F - 7 = 5S - 35
F = 5S - 35 + 7
F = 5S - 28

Next, substitute the value of F into the second equation:
(5S - 28) + 14 = 2(S + 14)
5S - 14 = 2S + 28
5S - 2S = 28 + 14
3S = 42
S = 42 / 3
S = 14

Now that we have the son's age, we can substitute S = 14 into the first equation to find the father's age:
F = 5S - 28
F = 5(14) - 28
F = 70 - 28
F = 42

Therefore, the present age of the father is 42, and the present age of the son is 14.