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Question 87
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 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 - (D)
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