# A two digit number is such that the product of its digits is 18 .when 63 is subtracted from the number, the digit interchange their place .find the number .

Solution: Let the tens digit be x. then ,the units digits =18/x

$\\\therefore number=10x+18/x$

Number obtained by interchanging the digits=10× 18/x +x

$\\ =10\times 18/x+x\\ \\\therefore (10x+18/x)-(10\times 18/x+x)=63\\ \\\Rightarrow 10x+18/x-180/x-x =63\\ \\\Rightarrow 9x^2-63x-162=0 \\ \\\Rightarrow x^2-7x-18=0$

$\\ \Rightarrow (x-9)(x+2)=0 \\ \\\Rightarrow x=9;or ;x=-2$

But , a digit can never be negative .so,x=9

Hence the requried number =$\\10\times 9+18/9=92$

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