| If a number of two digits is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by [GIC (AAO) 2011] |
A) \[9+k\]
B) \[10+k\]
C) \[11-k\]
D) \[k-1\]
E) None of these
Correct Answer: C
Solution :
| Let the number be \[10x+y.\] |
| Then, \[10x+y=k\,\,(x+y)\] ...(i) |
| Now, by interchanging the digits, we get the number \[10+x.\] |
| Now, \[10y+x=11y+11x-10x-y\] |
| \[=11\,\,(x+y)-k\,\,(x+y)\] [from Eq. (i)] |
| \[=(11-k)(x+y)\] |
| \[\therefore \]Number is \[(11-k).\] |
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