# The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number? - Mathematics

Sum
The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

#### Solution

Let us take the two-digit number such that the digit in the units place is b.
The digit in the tens place differs from b by 3.
Let us take it as b + 3.
So, the two-digit number is 10(b + 3) + b = 10b + 30 + b = 11b + 30.
With interchange of digits, the resulting two-digit number will be 10b + (b + 3) = 11b + 3.
If we add these two two-digit numbers, their sum is (11b + 30) + (11b + 3) = 11b + 11b + 30 + 3 = 22b + 33
It is given that the sum is 143.
Therefore, 22b + 33 = 143.
or 22b = 143 - 33
or 22b = 110
or b = 110/22
or b = 5
The units digit is 5 and therefore the tens digit is 5 + 3 which is 8. The number is 85.
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