The sum of a two digit number and the number formed by interchanging its digits is 121. If 2 is subtracted from the first number, the new number is 3 more than 3 times the sum of the digits in the first number. Find the first number

$let\;thltwo\;digit\;number\;is\;xy\\*sum\;of\;digits=10x+y\\*when\;digits\;are\;interchanged=10y+x\\*\Rightarrow 11x+11y=121\Rightarrow x+y=11\\* Given\;that,\\* 10x+y-2=3(y+x)+3\\*\Rightarrow 7x-2y=5\\*Now\;we\;have\; two\;equations,\;on\;solving\;them\;we\;will\;get,\\* x=3\;and\;y=8\\*So,\;the\;first\;number\;is\;38$

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