my son is x year old ,in five years time i will be twice his age and both our ages will be multiples of 10.the sum of ages will be between 50 and 100.how old am i

55

Well, well, well, seems like a number puzzle we've got here! Let's put on our thinking caps and solve it with a dash of humor!

If your son is currently "x" years old, we know that in five years, you'll be twice his age. That means your age would be 2x. And both of your ages will be multiples of 10.

Now, the sum of your ages is between 50 and 100. Let's do some detective work to narrow it down!

If we assume that your son is 5 years old now (since we don't know x), then in five years, he'll be 10 years old, and you'll be 2x.

Since both your ages need to be multiples of 10, the possible ages for you in five years are 20, 30, 40, etc. But remember, the sum of your ages needs to be between 50 and 100!

Let's try out the ages one by one with my trusty humor calculator:

For you at 20: 10 + 20 = 30 (too low)
For you at 30: 10 + 30 = 40 (still too low)
For you at 40: 10 + 40 = 50 (just right!)

There we have it! If your son is currently 5 years old, then you must be 40! But keep in mind, this is just one possibility, and there might be other solutions too. So, laugh it off and remember that numbers can sometimes be as funny as a clown! 🤡

Let's break down the information given:

1. Currently, your son is x years old.
2. In five years time, you will be twice his age, so your age in five years will be 2x.
3. Both your ages will be multiples of 10 in five years. This means both 2x and x must be divisible by 10.
4. The sum of your ages will be between 50 and 100.

From the second and third points, we can infer that both 2x and x must be multiples of 10. This means x must be a multiple of 10 as well.

Let's consider the possible values for x:

If x is 10, in five years your age will be 20, and the sum of your ages will be 10 + 20 = 30 (which is less than 50). Not a valid solution.

If x is 20, in five years your age will be 40, and the sum of your ages will be 20 + 40 = 60 (which is between 50 and 100). Therefore, you are currently 20 years old.

So, you are currently 20 years old.

To solve this problem, let's break it down step by step:

1. Let's assume your son's current age is represented by 'x'.
2. In five years, your son's age will be 'x + 5'.
3. According to the problem, your age in five years will be twice his age. So, your age will be '2 * (x + 5)'.
4. Both your ages in five years will also be multiples of 10. This means both 'x + 5' and '2 * (x + 5)' should be divisible by 10.
5. The sum of your ages (in five years) should be between 50 and 100. Therefore, 'x + 5 + 2 * (x + 5)' should satisfy this condition.

Now, let's solve the equation to find the value of 'x', which represents your son's current age:

x + 5 + 2x + 10 = 50 to 100

Combining like terms:

3x + 15 = 50 to 100

Subtracting 15 from both sides:

3x = 35 to 85

Now, we'll divide both sides by 3 to isolate 'x':

x = 35/3 to 85/3

However, since the ages of you and your son need to be whole numbers, we need to find an integer within this range that satisfies the given conditions.

The possible values for 'x' are:

- x = 12 (which would make your age 2 * (12 + 5) = 34)
- x = 13 (which would make your age 2 * (13 + 5) = 36)
- x = 14 (which would make your age 2 * (14 + 5) = 38)

Since there are multiple possible ages for you, the problem does not provide a unique solution.

son's age : (x+5) in 5 years.

Parent's age: 2(x+5) in 5 years.

50 < ((x+5) + 2(x+5))< 100,
50 < (x+5 + 2x+10) < 100,
50 < 3x+15 < 100,
50-15 < 3x < 100-15,
35 < 3x < 85,
35/3 < x < 85/3.
11 2/3 < X < 28 1/3,
16 2/3 < x+5 < 33 1/3,

(x+5) = 20 years = The son's age.

2(x+5) = 40 years = The parent's age.