Question

the
The digits of a 2-digit number, when written in reversed
form and Subtract from the original number,the
result is 36. If the sum of the digits is 10p the
original number is​

Answer 1

Step-by-step explanation:

Of course a unique solution to this problem could be calculated by considering the number to be xy, which is 10x + y. After reversing the number becomes yx, which is 10y + x. Asper given information, 10y+x - (10x+y) gives you 36, which is your equation @# 1 and x + y = 10 is your equation # 2. We have 2 variables and 2 equations and technically a unique solution is possible, unless there’s an inconsistency (which is not the case here) or unless both the equations come to once and the same (which is not the case here) or unless x and y turn out to be non-integers (which is not the case here).

This could be solved mentally too.

Let the number be xy. When, after reversing the digits the (new) number increases, we have x is strictly less than y. with x+y = 10 and x is strictly less than y, the only possibilities are:

19

28

37

46

With 19 and 91, the gap is much more than 36, so we discard it.

With 28 and 82, the gap is much more than 36, so we discard it.

With 46 and 64, the gap is much less than 36, so we discard it.

The only possibility remains is 37 and 73. The gap 73–37 = 36, matches with the requirement. Sum of digits is already 10.

Thus, 37 is the required answer.

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