Tricky Daughter and Mother's age-Math Riddle


Greetings, puzzle enthusiasts! Today, we delve into a delightful age mystery that revolves around the unique relationship between a mother and her daughter. The puzzle involves their ages, and the twist lies in the fact that the daughter's age is the reverse of her mother's. Join us as we unravel this charming age conundrum and embark on a journey to discover the ages of this intriguing mother-daughter duo.

 

The sum of a daughter and mother's age is 55. The age of the daughter is the mother's age reversed. Find the age of the mother and daughter, if the age of the mother is greater than 40 years.

 

Explanation :  

The total of the mother's age and the daughter's age is 50.
5 years ago, the mother was 7 times the age of the daughter.
Therefore,
If the total of their ages is 50 now, then 5 years ago the total of their ages was 40 (50 years minus 5 years off the mother's age and 5 years off the daughters age, or 50 (5+5)).
That last point is what will help us solve this problem. Let's state the last point as an equation. For the purposes of crafting some nice tidy equations,

M=Mother's age 5 years ago
D=Daughter' age 5 years ago
The first equation is pretty simple:
M+D=40
We also have to write the part about the mother being 7 times older than the daughter into an equation:
M=7D
Now that we have two equations, we can use them together to solve the question about how old the mother and daughter were 5 years ago. 
First, we can get rid of M to make the equation easier to solve.
Since M=7D, substitute the M in the first equation with 7D in the second equation:
M+D=40  > 7D+D=40
Now solve for D.
7D+D=40
8D=40
8D/8=40/8
D=5
So 5 years ago, the daughter was 5 years old. 
Now extrapolate:
5 years ago the daughter was 5, so now she's 10.
5 years ago, the mother was 7 times the age of her daughter (7D=M, or 7(5)=M), 
So, 5 years ago the mother was 35, and now she's 40 (7D+5=Mother's current age, or 7(5)+5=Mother's current age)
And if you need more proof,
40+10=50

 

 

 

In conclusion, the mystery of ages unfolds with the revelation that the mother is 49 years old, and the daughter is 6 years old. The numerical relationship between their ages adds a delightful twist to the world of mathematics. May this simple yet intriguing puzzle inspire a love for numbers and logic in your own mathematical adventures!


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