Question : The product of the digits of a two-digit number is 24. If we add 45 to the number, the new number obtained is a number formed by interchanging the digits. What is the original number?
Option 1: 54
Option 2: 83
Option 3: 38
Option 4: 45
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Correct Answer: 38
Solution :
Let the unit digit of the number be $y$ and the tens digit be $x$.
Number $= 10x$ + $y$
Product of digits $= x$ × $y = 24$ ---------------(i)
According to the question,
$10x+y+45 = 10y + x$
⇒ $9y-9x= 45$
⇒ $y-x = \frac{45}{9} = 5$ ---------------------(ii)
Solving equations (i) and (ii), we get,
$x= 3$ and $y= 8$
So, the number $=10x+y=10×3+8=38$
Hence, the correct answer is 38.
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