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If digits of a two-digit number are interchanged then the difference between the two number will be 63 and the product of the digits of the number is 8. Find the larger of the two numbers.  
1. 72
2. 78
3. 81
4. 92 

1 Answer

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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.

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