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If the number obtained on interchanging the digits of a 2 digit number is 18 more than the original number and the sum of the digit is 8.Then what is the original number?
- a)35
- b)53
- c)32
- d)34
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the number obtained on interchanging the digits of a 2 digit number...
Unit digit= x ; Ten’s digit = (8-x)
[10(8-x)+x] – [10x+(8-x)] = 18
80-10x+x-10x-8+x = 18
-18x = 18-80+8
18x = 54
X = 54/18 = 3
8 – x = 8 – 3 = 5
Hence the number is 35
[10(8-x)+x] – [10x+(8-x)] = 18
80-10x+x-10x-8+x = 18
-18x = 18-80+8
18x = 54
X = 54/18 = 3
8 – x = 8 – 3 = 5
Hence the number is 35
Most Upvoted Answer
If the number obtained on interchanging the digits of a 2 digit number...
Given Information:
The number obtained on interchanging the digits of a 2 digit number is 18 more than the original number and the sum of the digits is 8.
Solution:
Let the original number be 10x + y
Where x is the tens digit and y is the units digit.
According to the given conditions:
- The number obtained by interchanging the digits is 10y + x
- The new number is 18 more than the original number: 10y + x = 10x + y + 18
- The sum of the digits is 8: x + y = 8
Now, solving the above equations:
From x + y = 8, we can find that possible values for x and y are (2, 6) or (3, 5).
Let's check for (3, 5):
Substitute x = 3 and y = 5 in the equation 10y + x = 10x + y + 18:
10*5 + 3 = 10*3 + 5 + 18
53 = 35 + 18
53 = 53
Therefore, the original number is 35.
So, the correct answer is option A which is 35.
The number obtained on interchanging the digits of a 2 digit number is 18 more than the original number and the sum of the digits is 8.
Solution:
Let the original number be 10x + y
Where x is the tens digit and y is the units digit.
According to the given conditions:
- The number obtained by interchanging the digits is 10y + x
- The new number is 18 more than the original number: 10y + x = 10x + y + 18
- The sum of the digits is 8: x + y = 8
Now, solving the above equations:
From x + y = 8, we can find that possible values for x and y are (2, 6) or (3, 5).
Let's check for (3, 5):
Substitute x = 3 and y = 5 in the equation 10y + x = 10x + y + 18:
10*5 + 3 = 10*3 + 5 + 18
53 = 35 + 18
53 = 53
Therefore, the original number is 35.
So, the correct answer is option A which is 35.
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If the number obtained on interchanging the digits of a 2 digit number is 18 more than the original number and the sum of the digit is 8.Then what is the original number?a)35b)53c)32d)34Correct answer is option 'A'. Can you explain this answer?
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