| The difference between a two-digit number and the number obtained by interchanging the digits is 27. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1: 2? [Lie (AO) 2015] |
A) 10
B) 9
C) 11
D) 8
E) 6
Correct Answer: E
Solution :
| Let the digits at the two digits number be x and y, respectively. |
| Then, the number will be \[10x+y.\] |
| According to the question, |
| \[(10x+y)-(10y+x)=27\] |
| \[9x-9y=27\]\[\Rightarrow \]\[x-y=3\] |
| Given, \[y:x=1:2\]\[\Rightarrow \]\[x=2y\] |
| \[\therefore \] \[2y-y=3\] |
| \[\Rightarrow \] \[y=3\] and \[x=6\] |
| \[\therefore \] Number is 63 |
| Now, sum of digits \[=6+3=9\] |
| Difference of digits \[=6-3=3\] |
| \[\therefore \] Required difference \[=9-3=6\] |
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