Question 1163432: In a two digit number the tens digit is 3 more than the ones digit. If the digits are reversed the difference between the two numbers is 27. Find the number.
Thanks
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797)   (Show Source):
You can put this solution on YOUR website! .
In a two digit number the tens digit is 3 more than the ones digit. If the digits are reversed
the difference between the two numbers is 27. Find the number.
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Let "a" be the tens digit of the 2-digit number, and
let "b" be the ones digit of the number.
Then the number is
n = 10a + b, (1)
while the reversed digit number is
m = 10b + a. (2)
Since the tens digit is 3 more than the ones, the original number is greater than the reversed one.
Hence, according to the condition, the original number is 27 more than the reversed number. It means
(10a+b) - (10b+a) = 27, or
9a - 9b = 27,
9*(a-b) = 27,
a-b = 27/9 = 3. (3)
Notice that it is exactly the FIRST condition given in the problem.
Thus in the problem the first condition IS NOT INDEPENDENT: it is just contained in the second condition.
Surely, it is the problem's FAULT, which leads to the fact that the final solution is not unique.
Any of the numbers 41, 52, 63, 74, 85, 96 satisfies the problem's condition. ANSWER
Solved.
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Today I observe a FLOW of problems, part of which have curved formulation, while another part are simply INCORRECT.
It becomes really interesting to me, who creates these heavily sick problems and from which GARBAGE BOX the visitors recover them.
Probably, the time came to issue this WARNING:
If I will see the flow of nonsensical or heavy sick problems, I will collect their links
and write to the MANAGERS of this project asking them take PERSONAL measures against such visitors.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
There is not enough information given to find a unique answer. The problem is defective.
The difference between a 2-digit number and the number with the digits reversed is always 9 times the difference of the digits. Given that the difference of the digits is 3, we already know that the difference between the two numbers will be 9*3 = 27 -- so the information that the difference between the two numbers is 27 is superfluous.
But the only information given is those two dependent facts -- that the difference between the digits is 3 and the difference between the two numbers is 27. There is no other information given, making it impossible to find a unique answer.
Any 2-digit number with the tens digit 3 greater than the ones digit satisfies the given conditions.
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