The difference in the digits of a two digit number is 1.If the digits are interchanged,the number becomes 9 more than the old number.Find the number?

### Asked by arshijain | 8th Jun, 2020, 05:37: PM

Expert Answer:

###
Question must be: The sum of two digits of a two digit number is 9. If the digits are interchanged, the new number formed is 9 more than the original number. What is the number?

Solution:
Let x and y represent the ten's and unit's place of a number such that x>y.
The number is xy = 10x + y ... (i)
When the digits are interchenged, the number becomes yx = 10y+x
According to the question,
x + y = 9 ... (ii)
10y + x = 10x + y + 9
9y - 9x = 9
y - x = 1 ... (iii)
Solving (ii) and (iii), we get
x = 4 and y = 5

Question must be: The sum of two digits of a two digit number is 9. If the digits are interchanged, the new number formed is 9 more than the original number. What is the number?

### Answered by Renu Varma | 9th Jun, 2020, 10:15: AM

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