Question

XYZ is a 3 digit number such that when we calculate the difference between the two three digit number XYZ - YXZ the difference is exactly 90. How many possible values exist for the digits X and Y?

Answer 1

Answer:

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Answer 2

Given is the difference between two three-digit numbers XYZ and YXZ, Find the possible values of X and Y.

Explanation:

• First of all we get that the digits X and Y cannot accept the value of zero because both of them are occurring at the hundredth's place.
• Now expanding both the numbers in terms ones, tens, and hundreds we get,
• $XYZ=100X+10Y+Z,\ \ \ \ \ YXZ=100Y+10X+Z$  
• Now we are given the difference of both numbers,
• $XYZ-YXZ=90\\->100X+10Y+Z-100Y-10X-Z=90\\->90X-90Y=90\\->X-Y=1$  
• Therefore we can say that the values of X and Y are in consecutive order of numbers starting from one.
• The possible values of X and Y are, $(X,Y)->(2,1),(3,2),(4,3),(5,4),(6,5),(7,6),(8,7),(9,8)$
• Hence, there are existing eight possible values of both X and Y for the required scenario.