A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.

Let the one’s digit be ‘a’ and ten’s digit be ‘b’.


Given, two-digit number is such that the product of its digits is 20.


ab = 20 ----- (1)


Also, if 9 is added to the number, the digits interchange their places.


10b + a + 9 = 10a + b


a – b = 1 ----- (2)


Substituting value of a from eq1 in to eq2


20/b – b = 1


b2 + b – 20 = 0


(b + 5)(b – 4) = 0


Thus, b = 4 and a = b + 1 = 5


Number is 45.


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