The sum of the digits of a two digit number is 12. If 18 is added to it the digits are reversed. Find the number.
Answers
Answer:
your question is not clear.
Step-by-step explanation:
I’m not sure what you meant by what digits are reversed. Here are my answers based on my best guesses.
You meant “the digits are reversed; what is the original number?”
The solution can be obtained by letting x be the ‘tens digit’, and y be the unit digit, so that the original number is 10x+y.
Then 10x+y+18=10y+x, because the digits are reversed. This simplifies to 9x+18=9y, or x+2=y. Since the digits add up to 12, x+y=12. Substituting for y yields x+2=12-x, which simplifies to x=5. Then y=7, so the original number is 57. 57+18 = 75.
You’re asking what is the sum of the digits is if 18 is added to the original number. If the new number is a 2 digit number, the sum is still 12, but if it spills into 3 digits, the sum changes (84+18=102; sum is 3).
I’m pretty sure you meant #1, but i’m trying to be thorough.
The sum of the digits of a 2-digit number is 12. If the digits are reversed, the new number is 18 greater than the original number. What is the original number?
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The sum of digits of two digit number is 12. If the new number formed by reversing the digits is less than the original number by 54. Find the original number?
What is the original number if the sum of the digits of this two-digit number is 12, and, if the digits are reversed, the new number is 4/7 times the original number?
The sum of a particular two-digit number is 14. If this number's digits are reversed, the number is increased by 18. What is this number?
The simple way: Find all two digit candidates.
39, 48, 57, 66, 75, 84, 93
We know that it can't be 84 or 93, because adding 18 to one of those numbers would give us a three digit number as the result, not a two digit number with the digits reversed. So we're down to:
39, 48, 57, 66, 75
Try adding 18 to each of those numbers until you find the one that gets the digits reversed.
Of course there's a faster way: Realise that when you add 18 to another two digit number, it increases the first digit by 2 and decreases the second digit by 2. So we're looking for a number where the first digit is 2 smaller
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Call the digits of the number A and B (so the number is 10A+B). We know that A+B=12. Isolate B to get:
A=12-B
Then, we know that 18 plus our original number gets us reversed digits (10B+A), so we have: 18+(10A)+B=10B+A. Substitute in A=12-B to get:
18+(10(12-B))+B=10B+(12-B)
Start reducing and solve for B:
18+(120–10B)+B=10B+12-B
18+120–10B=10B+12–2B
138–10B=8B+12
126=18B
7=B
Substitute in to our original equation that A+B=12 and solve for A:
A+7=12
A=5
To check, our number would be 57. 57+18=75, so yes, the digits reverse.
Call the digits x and y . Then
x+y=12
10x+y+18=x+10y
From 2 we have 9x−9y=−18 so x−y=−2. Add this to equation 1 to find 2x=10, so x=5 and y=7. and yes, 57+18=75.
The sum of the digits of a two-digit number is 12. If the digits are interchanged, the number is increased by 18. What is the two-digit number?
The sum of the digits of a certain two-digit number is 15. When you reverse its digits, you increase the number by 27. What is the number?
The sum of the digits of a two-digit number is 18. If the digits are reversed, the number remains the same. What is the number?
The sum of the digits of a two-digit number is 11. If 9 is added to the number its digits are reversed. What is the number?
A 2-digit number is increased by 36 when the digits are reversed. The sum of the digits is 10. What is the original number?
The number is 57.
10a+b+18=10b+a
⟹(10a+b+18)−(a+b)=(10b+a)−(a+b)
⟹9b9=9a+189
⟶b=a+2
a+b=12
⟹a+(a+2)=12
⟹(2a+2)−2=12−2
⟹2a2=102
a=5
b=7
So the number is 57
Proof:
5+7=12
57+18=75
Both are valid.
Q.E.D.
There are 4 pairs of digits that add to 12: (3,9), (4,8), (5,7) and (6,6).These give 7 two digit numbers: 39,48, 57, 66, 75, 84, and 93.
If you add 18 to each of these the only one that reverses the digits is 57, as 57 + 18 = 75.
You can rearrange this to -75 + 18 = -57 if you want to consider negative numbers.
Let x be the one's digit and y be the ten's digit therefore number=10y+x
According to question,
X+Y=12….(1)
10y+x+18=10x+y
9y -9x=-18
Y-X=-2……(2)
(1)+(2)
2y=10
y=5
X=7
Therefore the number=57
Let no be 10y+x , x+y = 12
10y+x + 18 = 10x + y , or
x-y = 2
x+y = 12
So x = 7 , y = 5
So number is 57
The numbers are 57(5+7=12), and 75(7+5=12); 75–57=18
57.
5+7=12.
Add 18 to 57 = 75. (7+5=12 also). And 75 is 57 reversed.
The two-digit numbers are 39, 48, 57, 66, 75, 84, and 93.
Clearly, 57 and 75 only fulfill the condition.
5 and 7