| Let d be a two digit number. If half of d exceeds one-third of d by the sum of the digits in d, then the sum of the digits in d is [United India Insurance (AAO) 2012] |
A) 6
B) 8
C) 9
D) 15
E) None of these
Correct Answer: C
Solution :
| Let d be \[10x+y.\] |
| According to the question, |
| \[\frac{10x+y}{2}-\frac{10x+y}{3}=x+y\] |
| \[\Rightarrow \]\[3\,(10x+y)-2\,(10x+y)=6\,(x+y)\] |
| \[\Rightarrow \]\[30x+3y-20x-2y=6\,(x+y)\] |
| \[\Rightarrow \] \[10x+y=6\,\,(x+y)\] |
| \[\Rightarrow \] \[4x=5y\] |
| \[\Rightarrow \] \[\frac{x}{y}=\frac{5}{4}\] |
| Then, sum of digits can be 9 as \[(x+y)\]is in the multiple of \[(5+4=9).\] |
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