Question

1. The sum of the digits of a two-digit number is 15: The number obtained by interchanging its
digits exceeds the given number by 9. Find the original number.
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Answer 1

$\text{Let the number have x in its tens place and y in its ones place}\\\text{So the number is (10x+y) }\\\\\\\text{sum of the digit x+y is 15}\\\implies x+y=15\\\implies x=15-y---[1]\\\\\text{number when digits interchanged is 10y+x which exceeds 10x+y by 9}\\\implies (10y+x)= (10x+y)+9\\\implies9y-9x=9\\\implies y-x=1---[1] \\\\\\\text{substitite [1] in [2] }\\\\y-(15-y)=1\\\\y-15+y=1\\\\2y=16\\\\\boxed{\bold{y=8}}\\\\x=15-y\\\\x=15-8\\\\\boxed{\bold{x=7}}\\\\\\\textbf{\underline{The digit is 78}}$