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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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Most Upvoted Answer
The sum of the digits of a two digit number is 12. If the new number f...
Explanation:
The sum of the digits of a two-digit number is 12. Let the digits be x and y.
So, x + y = 12
When the digits are reversed, the new number is formed as 10y + x.
Given that the new number is greater than the original number by 54, we can write the equation as:
10y + x - 10x - y = 54
9y - 9x = 54
y - x = 6
Solving the equations:
From the first equation x + y = 12, we get y = 12 - x.
Substitute y = 12 - x in y - x = 6:
12 - x - x = 6
12 - 2x = 6
2x = 6
x = 3
Substitute x = 3 in x + y = 12:
3 + y = 12
y = 9
Therefore, the original two-digit number is 39.
So, the correct answer is option A - 39.
The sum of the digits of a two-digit number is 12. Let the digits be x and y.
So, x + y = 12
When the digits are reversed, the new number is formed as 10y + x.
Given that the new number is greater than the original number by 54, we can write the equation as:
10y + x - 10x - y = 54
9y - 9x = 54
y - x = 6
Solving the equations:
From the first equation x + y = 12, we get y = 12 - x.
Substitute y = 12 - x in y - x = 6:
12 - x - x = 6
12 - 2x = 6
2x = 6
x = 3
Substitute x = 3 in x + y = 12:
3 + y = 12
y = 9
Therefore, the original two-digit number is 39.
So, the correct answer is option A - 39.
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Community Answer
The sum of the digits of a two digit number is 12. If the new number f...
Let unit place digit be= x
Ten's place will be = 10x
Original number = 10x+x=12
Reversing the numbers= x+10x
According to question:
(x+10x)-54 = (10x+x)
11x=12+54
x=6
Original number=10×6+6=66
c) 66
Ten's place will be = 10x
Original number = 10x+x=12
Reversing the numbers= x+10x
According to question:
(x+10x)-54 = (10x+x)
11x=12+54
x=6
Original number=10×6+6=66
c) 66
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The sum of the digits of a two digit number is 12. If the new number formed by reversing thedigits 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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