Let the actual number be 10x+y.
Number on exchanging the digits will be 10y+x.
Now, 10y+x = 10x+y+27
=> 9y = 9x+27
Dividing the equation by 9.
y = x+3 (eqn i)
According to the question, x+y = 13
=> y = 13-x (eqn ii)
From eqn i and ii:
13-x = x+3
=> 10 = 2x
=> x = 10/2 = 5
Putting the value of x in eqn i:
y = x+3 = 5+3 = 8
Therefore the actual number was 10x+y = 10(5)+8 = 50+8 = 58.
Question : The sum of the digits of a two-digit number is 10. The number formed by reversing the digits is 18 less than the original number. Find the original number.
Option 1: 81
Option 2: 46
Option 3: 64
Option 4: 60
Question : By interchanging the digits of a two-digit number, we get a number that is four times the original number minus 24. If the unit's digit of the original number exceeds its ten's digit by 7, then the original number is:
Option 1: 29
Option 2: 36
Option 3: 58
Option 4: 18
Question : The tens digit of a two-digit number is larger than the unit digit by 7. If we subtract 63 from the number, the new number obtained is a number formed by the interchange of the digits. Find the number.
Option 2: 18
Option 3: 62
Option 4: 26
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