Answer :

Let the ones digit be ‘a’ and tens digit be ‘b’.


Given, two-digit number is such that the product of its digits is 8.


ab = 8 --- (1)


Also, when 18 is subtracted from the number, the digits interchange their places


10b + a – 18 = 10a + b


9b – 9a = 18


b – a = 2


b = 2 + a


Substituting in 1


a × (2 + a) = 8


a2 + 2a – 8 = 0


a2 + 4a – 2a – 8 = 0


a(a + 4) – 2(a + 4) = 0


(a – 2)(a + 4) = 0


a = 2


Thus, b = 4


Number is 42


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