Q. 195.0( 1 Vote )

A two - digit number is such that when it is multiplied by 9 then it will become double of number formed by interchanging the digits of the original number. If the difference of both the digits of the number is 7 then find the number.

Answer :

Let the digit in ten’s place be x and unit’s place be y


The difference between the two digit is 7


x - y = 7


x = y + 7 …equation (i)


When the digits are multiplied the resulting number is twice formed by interchanging the digits


2×(10x + y) = 9(10y + x)


20x + 2y = 90y + 9x


11x = 88y


x = 8y


Putting the value of x from equation (i) we get


y + 7 = 8y


7y = 7


y = 1


Putting the value in equation (i) we get


x = 8


So the two digit number is 18


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