100+ Challenging math riddles to keep your mind sharp

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

Explanation :  

Let's denote the word "FIVE" as $W$ and the process of removing the letters "F" and "E" as $R$. Mathematically, we can represent this as:

$W-R=IV$

Breaking it down:

1. $W$ represents the original word "FIVE."
2. $R$ represents the removal of the letters "F" and "E" from the word.

Substituting the value

$FIVE-(F+E)=IV$

This expression illustrates that by subtracting the letters "F" and "E" from the word "FIVE," we are left with the Roman numeral "IV," which symbolizes the number 4.

So, mathematically, the process can be represented as $FIVE-(F+E)=IV$.

 Answer: 72

 Explanation :  

Let's denote your house number as 

$X$ and your twin brother's house number as $Y$. According to the given conditions:

1. Both house numbers have the same digits '1' and '9':$X=19$ and $Y=91$.
2. The difference between your house numbers is $Y-X$.

Substituting the values:

$Y-X=91-19=72$

So, mathematically, the explanation can be represented as $Y-X=72$, where $X=19$ and  $Y=91$. This illustrates that the house numbers 19 and 91 indeed have the same digits '1' and '9', and the difference between them is 72.

Two

Explanation :  

The inside and the outside.

Answer: 86

Explanation :  

Let's denote the original number as $N$. When this number is turned upside down and flipped, it becomes a different number, denoted as ′N′.

When the original number, $N$, is turned upside down and flipped, it becomes N′. According to the given problem:

N′=98

The problem also specifies that ′N′ is 12 more than the original number, $N$:

N′=N+12

From the previous equation, we know that ′=98N′=98, so we can substitute this value into the equation:

$98=N+12$

Now, to find the original number, $N$, we need to solve for $N$:

$N=98-12$

$N=86$

Hence, the original number, when turned upside down and flipped, becomes 98, which indeed is 12 more than 86.

This mathematical explanation confirms that the number in question is 86, as it satisfies the conditions provided in the problem.

Explanation :  

One has three letters in the word three has five letters in it five has four letters and four has four letters in it (if you try more numbers they will always come back to the number four: so four is the magic number.

    150 apples . 

    Explanation :  

    Paul 15 apples, Nick 50, and Ben 85.  
    Sell the apples in such a way that each  brings home the same amount of money. 
    Let say Amount brought them by = N Let say A , 
    B & C are the Prices at which they sell apples 
    N = 15A 
    N = 50B 
    N = 85C 
    N least value is LCM of  15, 
    50  & 85 15  = 3 * 5 50 = 2 * 5 * 5 85 = 5 * 17 
    LCM = 2 * 3 * 5 * 5  * 17 LCM  = 2550 
    A = 170      
    B = 51      
    C = 30 
    Paul Sell apple at Rs 170 each Nick Sell Apple at Rs 51 Each Ben sell Apple at  Rs 30 
    Each They will Sell apple at price in Ratio 170 : 51  : 30  

King Tut was born in 20 B.C. 

Explanation :  

There were 120 years between the birth of King Eros and the death of King Tut, but since their ages amounted to only 100 years, there must have been 20 years when neither existed. This would be a period between the death of King Eros, 40 B.C., and the birth of King Tut, 20 B.C.

    48

    Explanation :  

    The length of the fish is 48

    Let x = length of fish
     
    Then, ½x = length of body
                6 + (½)(½x) = 6 + ¼x = length of tail
     
    Length of fish = length of head + length of body + length of tail
     
    x = 6 + ½x + 6 + ¼x
     
    x = 12 + ¾x
     
    ¼x = 12
     
    x= 48

1,2,3

Explanation :  

The three different whole numbers whose sum is equal to their total when multiplied are 1, 2, and 3.
1 + 2 + 3 = 6 and 
1 * 2 * 3 = 6

50

Explanation :  

50 steps Each forward step = 30cm  
Each backward step = 40cm  
If monkey climbed 3 steps, means it covering 3*30=90cm  
If monkey slips 2 steps means = 2*40 = 80cm 
then monkey covers only 10cm.  
Therefore for covering 10 cm monkey has to take 5 steps. 
Then for climbing 100 cm tree it takes  100 ÷ 10 = 10cm  
For covering 100cm, it should take 5*10 = 50 steps.

Answer: Minimum of 12 apples

Explanation :  

Let the number of children be X,
Therefore, the number of apples bought by Tanya = ( X + 1) 
The total number of apples in the shop A = ( X + 1) 
Total number of apples bought by Trader Tarun =  2( X + 1 ) 
Total number of apples in the carton = 4( X + 1 ) 

Now, the minimum no. of apples in a carton: 
We assume:  X is not equal to 0  
X is not equal to 1 ( Tanya has children not a single child)  
X  equal to 2  (Tanya has a minimum of 2 children) 

When X = 2
Let the number of children be X
Therefore, the number of apples bought by Tanya = ( X + 1)
The total number of apples in the shop A = ( X + 1)
Total number of apples bought by Trader Tarun = 2( X + 1 )
Total number of apples in the carton = 4( X + 1 )
Now, minimum no of apples in carton:
We assume:
X is not equal to 0
X is not equal to 1 ( Tanya has children not a single child)
X equal to 2 (Tanya has a minimum of 2 children)
When X = 2
4( X + 1 )
= 4( 2 + 1 )
= 12
Thus, minimum of 12 apples

Answer: 11 cartons.

Explanation :  

If we take into account that Tom shipped both large as well as small boxes in the cartons.

If a total of 96 boxes are shipped then the large boxes in the cartons must be a multiple of 8 which means either 16 or 56 large boxes are there.

But according to the question that there are more large boxes in the cartons then the small ones, so the number of large boxes must be 56.

And therefore the number of small boxes are reduced to 96 - 56 = 40

So the total number of cartons shipped are:

56/8 + 40/10 = 7 + 4 = 11

977 animals

Explanation :  

977 animals (100×2 = 200; 200+800 = 1000; 1000-23 = 977)

1, 2, and 3.

Explanation :  

1,2 and 3 As:
1+2+3=6
and
1*2*3=6
1,2 and 3 are the positive integers and the result of their addition and their multiplication is same.