Question 93

Product of digits of a 2-digit number is 24. If we add 45 to the number, the new number obtained is a number formed by interchange of the digits.What is the original number?

Solution

Let the unit's digit of the number be $$y$$ and ten's digit be $$x$$

=> Number = $$10x + y$$

Product of digits = $$x \times y = 24$$ --------------(i)

According to question, => $$10x + y + 45 = 10y + x$$

=> $$9y - 9x = 45$$

=> $$y - x = \frac{45}{9} = 5$$ --------------(ii)

Solving equation (i) and (ii), we get : $$x = 3$$ and $$y = 8$$

$$\therefore$$ Number = 38

=> Ans - (C)

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