## Check Filling Error

On the check it was written:… xxxABx

But the correct would be:… xxxBAx

That is, in the tens of check was written B (that's what we want to find).

Therefore the person paid R $ 270,00 more, so doing the subtraction the result will be 270:

… Xxx**AB**x

… Xxx**BA**x

----------------

… 000**27**0

Therefore we must have AB - BA = 27

The exercise says that A and B are with each other as 1 is for 2. Hence we know that A is twice B, ie: **A = 2B**.

Knowing this, there are 4 possible values for A and B:

**B = 1 and A = 2** => 21-12 = 9 => this can't be (since AB-BA = 27)**B = 2 and A = 4** => 42-24 = 18 => this can't be (since AB-BA = 27)**B = 3 and A = 6** => 63-36 = **27** => these are the values (because **AB-BA = 27**)**B = 4 and A = 8** => 84-48 = 36 => this can't be (since AB-BA = 27)

Therefore the values are A = 6 and B = 3.

**Answer: The digit written on the check in the tens was 3.**

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