What is car plate no if last digit is double of first, second & third are same, last two is double of first two digits

Question

Its a 4 digit Car Plate Number: KL45 - _ _ _ _
1. Last digit is double of First digit.
2. Second digit & Third digits are the same.
3. Last two digit is the double of the First Two digit.

So whats the Car plate No.
KL45 - _ _ _ _

Answer 1

let the first digit be X. Possible numbers of X are 1 , 2 , 3 and 4
So the last digit wil be 2X.
The second and third digits are the same. Let that be y.
The car plate number is of the form X Y Y 2X
Now, 2 ( first two digits) = Last two digits.
Substituting the values,
2 ( 10X + Y) = 10Y + 2X
20x + 2y = 10 y + 2x ==> 18x = 8y ==> y = 9/4 (x)
So the only possible number of x = 4 , which gives value of y as 9.
The number plate value will be 4 9 9 8
Thus,
KL45-4998 is the car plate number

Comments

1224 also satisfy

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1224 does not satisfy the first condition i.e. last digit is double of first digit :)

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And the 3rd condition.