if a boy is 24 year younger than his father and after two years the sum of their ages will be 40.how old is the father?

Let f = age of father

and(f-24) = age of son
After two years their sum of ages will be 40. So,
(f+2) + (f-24) + 2 = 40
2f - 20 = 40
2f = 40 + 20
2f = 60
father(f) = 30 yrs

Well, if a boy is 24 years younger than his father, then the father's age must be, umm... 24 years older than the boy's age. It's like a code, you see, they're always 24 years apart.

Now, let's solve this puzzle. In two years, the sum of their ages will be 40, right? Hmm, let me do some calculations here... So, if we add 2 years to their current ages, it should give us 40.

Let me grab my imaginary calculator...beep boop beep... Yep, got it! So, if the sum is going to be 40 in two years, then the boy's age must be 14 and the father's age must be... wait for it... 38!

Voila! The father is 38 years old. Guess that's why they say, age is just a number until you start doing math, am I right?

Let's break down the problem step by step:

Step 1: Let's assign variables to represent the ages of the boy and his father.
Let's say the boy's age is x and the father's age is y.

Step 2: According to the problem, the boy is 24 years younger than his father.
This can be written as: x = y - 24.

Step 3: After two years, the sum of their ages will be 40.
In two years, the boy's age will be x + 2 and the father's age will be y + 2.
So we have the equation: (x + 2) + (y + 2) = 40.

Step 4: Now we can substitute the value of x from the first equation into the second equation.
Substituting x = y - 24, we get:
(y - 24 + 2) + (y + 2) = 40.

Simplifying this equation, we can combine like terms:
2y - 20 = 40.

Step 5: Now let's isolate the variable by moving the constant term to the other side.
Adding 20 to both sides, we get: 2y = 60.

Step 6: Finally, solve for y by dividing both sides by 2:
y = 30.

Therefore, the father is 30 years old.

To find the current age of the father, we can set up an equation based on the information given.

Let's assume the current age of the boy is B and the current age of the father is F.

According to the given information:
1. "A boy is 24 years younger than his father" can be written as: B = F - 24
2. "After two years, the sum of their ages will be 40" can be written as: (B + 2) + (F + 2) = 40

Now, we can substitute the value of B from the first equation into the second equation to solve for F:

(F - 24 + 2) + (F + 2) = 40
F - 22 + F + 2 = 40
2F - 20 = 40
2F = 60
F = 60 / 2
F = 30

Therefore, the current age of the father is 30 years old.