Correct Answer - Option 3 : 81
Given :
Difference between original and new number = 63
Product of digits = 8
Concept used :
If 'x' is the digit at the one's place and 'y' at the ten's place the digit will become '10y + x' and the digit after interchange will become '10x + y'
Calculations :
Let the two-digit number '10y + x'
The number after digits interchanged will be '10x + y'
According to the question
10y + x - (10x + y) = 63
9y - 9x = 63 '
⇒ y - x = 7
Numbers of this type can be (81,18) and (92, 29)
But we know that the product of x and y is 8
⇒ So the only possible value will be (81,18)
⇒ So the required number = 81
∴ Option 3 will be the correct choice.