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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?
Most Upvoted 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
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Community 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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