# I am a number greater than 40,000 and less than 60000. my ones digit and tens digit are the same. my ten thousand digit is 1 less than 3 times the sum of my ones digit and tens digit. my thousand digit is half my hundreds digit and the sum of these two digits is 9. what number am i?

$Let\;the\;number\;be\;abcdd\\* then,\\* \indent a=3(d+d)-1\\* \indent a = 6d-1\\*Now,\;try\;to\;find\;value\;of\;d\;by\;hit\;and\;trial\;method\\* for, d=1\Rightarrow a=5\\* and,\; d=2\Rightarrow a=11\\* a\;is\;single\;digit,\;so,\;d=1\;and\;a=5\\* Now,\\* \indent b=\frac{c}{2} \Rightarrow 2b=c\\* and, \;b+c=b+2b=3b\\* \Rightarrow 3b=9\\*\Rightarrow b=3\;and\;c=6\\* Hence,\;number\;is\;53611$

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