Ok, It is riddle. Jack is married to Jill. There son wants to know their age. Jack says,"if you reverse the digits in my age, you get your mother's. Jill said" The sum of my age is your dad's age equal to 11 times the difference in oour ages. Remember that I am older than your mother. What are Jack and Jill's ages?
they r 10 and11
To solve this riddle and determine Jack and Jill's ages, we can follow these steps:
1. Let's assume Jack's age is a two-digit number. We'll represent it as AB, where A and B are the digits representing his age.
2. According to Jack's statement, if we reverse the digits of his age, we get Jill's age. Since Jill is older, her age must be greater than Jack's, so the reversed digits of his age will be BA.
3. This implies that Jill's age is BA, and according to her statement, the sum of her age and Jack's age (AB) is equal to 11 times the difference in their ages.
4. Therefore, we can write an equation as follows:
AB + BA = 11 * |BA - AB|
Let's solve this equation step by step:
5. Since AB represents a two-digit number, we can rewrite it as 10A + B.
Similarly, BA can be rewritten as 10B + A.
6. Substituting these values into the equation, we have:
10A + B + 10B + A = 11 * |(10B + A) - (10A + B)|
7. Simplifying both sides of the equation:
11A + 11B = 11 * |9B - 9A|
8. Dividing both sides by 11:
A + B = |9B - 9A|
9. Since we know A and B are single-digit positive integers (0-9), we can try different values for A and B and check which combinations satisfy the equation.
10. By testing different values, we find that A = 4 and B = 9 is a valid solution:
4 + 9 = |9 * 9 - 9 * 4|
11. Therefore, Jack's age (AB) is 49, and Jill's age (BA) is 94.
Thus, Jack is 49 years old, and Jill is 94 years old.