Question

A house wife forgot her bank ‘ATM PIN’ which is four digits number, but luckily she remembered some hints on how to recall this ‘PIN’. Here are some of the clues 1) The 1st digit is a 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 the digits is 23 What is the ATM PIN?

Answer 1

Let the digits of the ATM PIN be as follows
1st = a
2nd = b
3rd = c
4th = d

Given
a + b + c + d = 23 --------------(1)
b + c = 10 ------------------------(2)

Substitute the value of (2) in (1)
=> a + 10 + d = 23
=> a + d = 13 -------------------(3)

Given
d = b + 1 -------------------------(4)

Substitute (4) in (3)
=> a + b + 1 = 13
=> a + b = 12 -------------------(5)

Given b = 2a ['a is half of b' can be written as b is twice of a]

Substitute value of a in (5)
=> a + 2a = 12
=> 3a = 12
=> a = 4
b = 2a = 2(4) = 8

Substitute value of b in (2)
=> 8 + c = 10
=> c = 2

Substitute values of a, b and c in (1)
=> 4 + 8 + 2 + d = 23
=> 14 +d = 23
=> d = 9

Therefore the ATM PIN is 4829

Hope it helps

Answer 2

Answer ;

${ \large{ \underline{ \sf{ \pmb{Given...}}}}}$

★ The first digit is half of the second

★ The sum of second digit and third digit is 10

★ The 4th is equal to the second plus 1

★ The sum of all digits is 23

${ \large{ \underline{ \sf{ \pmb{To \: Find ...}}}}}$

★ The ATM pin [ The number]

${ \large{ \underline{ \sf{ \pmb{Solution ...}}}}}$

★ The ATM pin is 4829

${ \large{ \underline{ \sf{ \pmb{Full \: Solution ...}}}}}$

~ As we have given the clues about the digits of the ATM pin let's assign a suitable variable with some constants which make the given statement true

➼ Let's assign the following values to the digits

1st digit = x

2nd digit = 2x

3rd digit = 10 - 2x

4th digit = 2x + 1

★According To The Question :

✪ The sum of all the digits is 23

~Now let's frame an equation adding up the assigned values letting the sum to be 23

$</h3><h3>{ \underline{ \bf{ \bigstar{Framing \: an \: equation \: we \: get : }}}}$

$\begin{gathered}{ : \implies} \sf \: x + 2x + 10 - 2x + 2x + 1 = 23 \\ \\ \\ { : \implies} \sf 3x + 10 - 2x + 2x + 1 = 23 \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf 10 + 1 + 3x - 2x + 2x = 23 \: \: \: \: \: \\ \\ \\ { : \implies} \sf 11 + x + 2x = 23 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf 11 + 3x = 23 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf 3x = 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf x = \cancel\frac{12}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf { \purple{ \underline{ \boxed{ \pmb{ \frak{x = 4}}} }\bigstar}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered} </p><p>:⟹x+2x+10−2x+2x+1=23</p><p>:⟹3x+10−2x+2x+1=23</p><p>:⟹10+1+3x−2x+2x=23</p><p>:⟹11+x+2x=23</p><p>:⟹11+3x=23</p><p>:⟹3x=12</p><p>:⟹x= </p><p>3</p><p>12</p><p> </p><p> </p><p> </p><p> </p><p>:⟹ </p><p>x=4</p><p>x=4$

★ Henceforth the Value of x is 4

~Now let's find the digits of the pin

• First Digit :

${ : \implies} \sf 1st \: digit = x = 4:⟹1stdigit=x=4$

• Second Digit :

$</p><p></p><p>{ : \implies} \sf 2nd \: digit = 2x = 2(4) = 8:⟹2nddigit=2x=2(4)=8$

• Third Digit

$</p><p></p><p>{ : \implies} \sf 3rd \: digit = 10 - 2x = 10 - 2(4) = 2:⟹3rddigit=10−2x=10−2(4)=2$

• Fourth Digit :

${ : \implies} \sf 2x + 1 = 2(4) + 1 = 9:⟹2x+1=2(4)+1=9$

Henceforth the ATM pin number is 4829