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The number obtained by interchanging the two digits of a two digit number is less than the original number by 27. If the difference between the two digits of the number is 3, then what is the original number?
- a)64
- b)72
- c)65
- d)73
- e)None of the Above
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
The number obtained by interchanging the two digits of a two digit num...
original number – 10x + y
(10x + y) – (10y + x) = 27
9(x – y) = 27
x – y = 3
All the given options not follow the condition.
(10x + y) – (10y + x) = 27
9(x – y) = 27
x – y = 3
All the given options not follow the condition.
Most Upvoted Answer
The number obtained by interchanging the two digits of a two digit num...
Consider only the last number of the statement. If you use this for any of the options, the difference of the digits will not be equal to 3. Hence, none of the above.
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Community Answer
The number obtained by interchanging the two digits of a two digit num...
Given information:
- The number obtained by interchanging the two digits of a two-digit number is less than the original number by 27.
- The difference between the two digits of the number is 3.
Let's assume the original two-digit number to be xy, where x represents the tens digit and y represents the units digit. Therefore, the number obtained by interchanging the digits would be yx.
From the given information, we can form the following equations:
- xy - yx = 27 (since the interchanged number is less than the original number by 27)
- x - y = 3 (since the difference between the digits is 3)
Simplifying the first equation, we get:
- 10x + y - (10y + x) = 27
- 9x - 9y = 27
- x - y = 3
We can see that the second equation is the same as the simplified form of the first equation. This means that we only have one equation and two variables. Therefore, we cannot determine the original number uniquely.
Let's solve for x in terms of y using the second equation:
- x = y + 3
Substituting this into the first equation:
- (y + 3) - y = 3
- 3 = 3
This is a tautology, which means that the equation is true for all values of y. Therefore, there are infinitely many two-digit numbers that satisfy the given conditions.
Hence, the correct answer is option E, None of the Above.
- The number obtained by interchanging the two digits of a two-digit number is less than the original number by 27.
- The difference between the two digits of the number is 3.
Let's assume the original two-digit number to be xy, where x represents the tens digit and y represents the units digit. Therefore, the number obtained by interchanging the digits would be yx.
From the given information, we can form the following equations:
- xy - yx = 27 (since the interchanged number is less than the original number by 27)
- x - y = 3 (since the difference between the digits is 3)
Simplifying the first equation, we get:
- 10x + y - (10y + x) = 27
- 9x - 9y = 27
- x - y = 3
We can see that the second equation is the same as the simplified form of the first equation. This means that we only have one equation and two variables. Therefore, we cannot determine the original number uniquely.
Let's solve for x in terms of y using the second equation:
- x = y + 3
Substituting this into the first equation:
- (y + 3) - y = 3
- 3 = 3
This is a tautology, which means that the equation is true for all values of y. Therefore, there are infinitely many two-digit numbers that satisfy the given conditions.
Hence, the correct answer is option E, None of the Above.
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