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  • 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 .

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 .

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

\ herefore number=10x+18/x

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

\ =10 imes 18/x+x\ \ herefore (10x+18/x)-(10 imes 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 imes 9+18/9=92

 

Posted by

Deependra Verma

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