## 4. The sum of the digits of a 2-digit number is 10. If 36 is subtracted from the number, the result is a number whose digits are

Question

4. The sum of the digits of a 2-digit number
is 10. If 36 is subtracted from the number,
the result is a number whose digits are
interchanged as compared to the original
number. Find the numbers.​

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2 months 2021-09-25T05:25:11+00:00 1 Answer 0 views 0

73

Step-by-step explanation:

Well, let the tens place and ones place digits in the number be respectively    and   , which are each between 0 and 9 inclusive. Then the number itself is equal to  10+ . Now add 36 to the number, and we have  10++36=10+ , where the last part of the equality follows from the reversal of the digits.

The above equation simplifies to  9+36=9 .

This simplifies to  9(+4)=9 , or  +4= .

We need a second equation in order to get a unique solution. The original question says that “the sum of the two-digit number is 10.” This is poorly-worded, but I think what it means is that the sum of the digits in the two-digit number is 10. If that’s true, then  +=10 . Since  +4=,  this becomes  2+4=10 . I.e.  2=6 , or  =3 . Thus  =+4=7.

The number is 37. Check this answer:

37+36=73

which is indeed a reversal of the digits.