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A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Then the original number is _____.
- a)53
- b)45
- c)92
- d)63
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number consists of two digits whose sum is 9. If 27 is subtracted fr...
Let units place digit be x. So tens place digit = 9 − x.
∴ The original number = 10(9-x)+x = 90-10x + x=90 - 9x Now, after interchanging the digits, the number formed = 10 (x) + 9 - x = 9x + 9
∴ According to question, we have 90 - 9x - 27 = 9x + 9
⇒ −18x = −54 ⇒ x = 3
So, the original number
= 90−9×3 = 63
Most Upvoted Answer
A number consists of two digits whose sum is 9. If 27 is subtracted fr...
Given information:
- The sum of two digits is 9
- When 27 is subtracted from the original number, its digits are interchanged
To find:
The original number
Solution:
Let the two digits be x and y, where x is the tens digit and y is the ones digit. We know that x+y=9.
So, x=9-y.
The original number can be written as 10x+y, and the number with interchanged digits can be written as 10y+x.
According to the given information, when 27 is subtracted from the original number, its digits are interchanged. Therefore, we have the equation:
10x + y - 27 = 10y + x
Substituting x=9-y in the above equation, we get:
10(9-y) + y - 27 = 10y + (9-y)
90 - 9y + y - 27 = 10y + 9 - y
63 = 18y
y = 3.5
Since y has to be a whole number, this is not a valid solution. Therefore, there is no integer solution for the two digits whose sum is 9 and whose digits are interchanged when 27 is subtracted.
However, we can check the answer choices to see which one satisfies the given conditions:
- Option A: 53. Sum of digits = 5+3 = 8, which is not equal to 9. This is not a valid solution.
- Option B: 45. Sum of digits = 4+5 = 9. When 27 is subtracted, we get 18, which has digits interchanged as 81. Therefore, this is a valid solution.
- Option C: 92. Sum of digits = 9+2 = 11, which is not equal to 9. This is not a valid solution.
- Option D: 63. Sum of digits = 6+3 = 9. When 27 is subtracted, we get 36, which has digits interchanged as 63. Therefore, this is a valid solution.
Therefore, the original number is 63, which is option D.
- The sum of two digits is 9
- When 27 is subtracted from the original number, its digits are interchanged
To find:
The original number
Solution:
Let the two digits be x and y, where x is the tens digit and y is the ones digit. We know that x+y=9.
So, x=9-y.
The original number can be written as 10x+y, and the number with interchanged digits can be written as 10y+x.
According to the given information, when 27 is subtracted from the original number, its digits are interchanged. Therefore, we have the equation:
10x + y - 27 = 10y + x
Substituting x=9-y in the above equation, we get:
10(9-y) + y - 27 = 10y + (9-y)
90 - 9y + y - 27 = 10y + 9 - y
63 = 18y
y = 3.5
Since y has to be a whole number, this is not a valid solution. Therefore, there is no integer solution for the two digits whose sum is 9 and whose digits are interchanged when 27 is subtracted.
However, we can check the answer choices to see which one satisfies the given conditions:
- Option A: 53. Sum of digits = 5+3 = 8, which is not equal to 9. This is not a valid solution.
- Option B: 45. Sum of digits = 4+5 = 9. When 27 is subtracted, we get 18, which has digits interchanged as 81. Therefore, this is a valid solution.
- Option C: 92. Sum of digits = 9+2 = 11, which is not equal to 9. This is not a valid solution.
- Option D: 63. Sum of digits = 6+3 = 9. When 27 is subtracted, we get 36, which has digits interchanged as 63. Therefore, this is a valid solution.
Therefore, the original number is 63, which is option D.
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A number consists of two digits whose sum is 9. If 27 is subtracted fr...
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A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Then the original number is _____.a)53b)45c)92d)63Correct answer is option 'D'. Can you explain this answer?
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