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The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.
- a)39
- b)57
- c)66
- d)93
Correct answer is option 'A'. Can you explain this answer?
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The sum of the digits of a two digit number is 12. If the new number f...
Problem Analysis:
Let's assume the original number is represented as "10a + b" where 'a' is the tens digit and 'b' is the units digit. The reversed number would be "10b + a". Given that the sum of the digits is 12, we can write the equation as:
a + b = 12
The new number formed by reversing the digits is greater than the original number by 54, so we can write the equation as:
(10b + a) - (10a + b) = 54
Simplifying the equation, we get:
9b - 9a = 54
Dividing both sides by 9, we get:
b - a = 6
Now we have a system of equations:
a + b = 12
b - a = 6
Solving the System of Equations:
We can solve the system of equations by either substitution or elimination method.
Substitution Method:
From the second equation, we can express 'b' in terms of 'a':
b = a + 6
Substituting this value of 'b' in the first equation, we get:
a + (a + 6) = 12
2a + 6 = 12
2a = 6
a = 3
Substituting the value of 'a' back into the second equation, we get:
b - 3 = 6
b = 9
Therefore, the original number is 39.
Answer:
The original number is 39, which matches with option A.
Let's assume the original number is represented as "10a + b" where 'a' is the tens digit and 'b' is the units digit. The reversed number would be "10b + a". Given that the sum of the digits is 12, we can write the equation as:
a + b = 12
The new number formed by reversing the digits is greater than the original number by 54, so we can write the equation as:
(10b + a) - (10a + b) = 54
Simplifying the equation, we get:
9b - 9a = 54
Dividing both sides by 9, we get:
b - a = 6
Now we have a system of equations:
a + b = 12
b - a = 6
Solving the System of Equations:
We can solve the system of equations by either substitution or elimination method.
Substitution Method:
From the second equation, we can express 'b' in terms of 'a':
b = a + 6
Substituting this value of 'b' in the first equation, we get:
a + (a + 6) = 12
2a + 6 = 12
2a = 6
a = 3
Substituting the value of 'a' back into the second equation, we get:
b - 3 = 6
b = 9
Therefore, the original number is 39.
Answer:
The original number is 39, which matches with option A.
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The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.a)39b)57c)66d)93Correct answer is option 'A'. Can you explain this answer?
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