Question : The product of the digits of a 2-digit number is 12. If we add 36 to the number, the new number obtained is a number formed by the interchange of the digits. What is the number?
Option 1: 62
Option 2: 34
Option 3: 26
Option 4: 43
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Correct Answer: 26
Solution :
Let the unit digit of the number be $y$ and the ten digit be $x$.
Number $= 10x + y$
Product of digits $= x × y = 12$ ---(i)
According to the question,
$10x + y + 36=10y + x$
$9y – 9x = 36$
$y – x = \frac{36}{9} = 4$ ---(ii)
Solving equations (i) and (ii),
$x = 2, y = 6$
∴ Number $=$ 26
Hence, the correct answer is 26.
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