## HOW TO RECALL FORGOTTEN PIN OF ATM CARD

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__Solve this maths in 5 mins__

__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?**

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__Solution__

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

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**According to 1st condition**

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

### 2nd condition

The sum of the 2nd and 3rd is 10 i.ex + y = 10

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

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**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 )

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1st of all we have to find the value of x .because x is related to all other equations.

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**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 = 233x/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

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y = 2 **This is our 3rd digit**

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**So The PIN Would be wxyz ➡️4829**

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Verification

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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