## Solve this maths in 5 mins

A house wife forgot her 'ATM PIN' which is a four digit number, but luckily she remembers some hints on how to recall this 'PIN'
Here are some of the clues

1. The 1st digit is half of the 2nd
2. The sum of the 2nd and 3rd is 10
3. The 4th is equal to the 2nd plus 1
4. The sum of all digits is 23

What is her ATM PIN?

## Solution

Let the four digits PIN be   wxyz, Here 1st ,2nd .3rd and 4th digit are w,x,y and z  respectively .

### According  to 1st condition

The 1st digit is half of the 2nd i.e
w = x/2   .......................................... (1 )

### 2nd condition

The sum of the 2nd and 3rd is 10 i.e

x + y = 10

This implies   y = 10 - x  .................... ( 2 )

### 3rd condition

The 4th is equal to the 2nd plus 1    i . e

z = x + 1     .......................... ( 3 )

### According  to 4th condition

The sum of all digits is 23 . i e .

w  +  x + y + z  = 23 ............ ( 4 )

### How to find 2nd digit

1st of all we have to find the value of x .because x is related to all other equations.
Putting the values of w ( from eq1) , y (from eq 2), z( from eq3) in ( 4) we get
x/2   + x + 10 - x + x + 1 = 23,cancelling 'x'

3x/2 +11 = 23
3x/2 =23-11
3x/2 = 12

x = 8 This is our 2nd  digit

Now put the value of x in  (1)
w = 8/2
w = 4  ,This is our 1st  digit

To find 3rd digit Put the value of x in (3)
z = x + 1
z = 8 + 1
z = 9 This is our 4th  digit
To find 3rd digit Put the value of x in (2)
y = 10 - 8

## Verification

1 The 1st digit is half of the 2nd      ➡️   4  and  8 , definitely 4 is half of 8

2. The sum of the 2nd and 3rd is 10  ➡️ 8+2 =10
3. The 4th is equal to the 2nd plus 1  ➡️ 9 = 8+1
4. The sum of all digits is 23   ➡️ 4 + 8 + 2 + 9 = 23

## Conclusion

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