Q. 163.9( 11 Votes )

A two - digit number is such that the product of its digits is 35. If 18 is added to the number, the digits interchange their places. Find the number.

Answer :

Let the two - digit number be xy (i.e. 10x + y).


After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).


According to question -


xy = 35


x = 35/y.....(1)


and,


(10x + y) + 18 = (10y + x)


9x - 9y = - 18


x - y = - 2.....(2)


Substituting the value of x in equation (2), we get -



35 - y2 = - 2y


y2 - 2y - 35 = 0


y2 - 7y + 5y - 35 = 0


y(y - 7) + 5(y - 7) = 0


(y + 5)(y - 7) = 0


y = 7


[y = - 5 is invalid because digits of a number cannot be negative.]


Substituting the value of y in equation (1), we get -


x = 5


Thus, the required number is 57.


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