Question
Download Solution PDFThe difference between a two-digit number and the number obtained by interchanging the two digits of the number is 9. What is the difference between the two digits of the number?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The difference between a two-digit number and the number obtained by interchanging its digits is 9.
Formula used:
Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.
The number obtained by interchanging the digits is 10y + x.
Difference = (10x + y) - (10y + x) = 9
Difference between two digits = |x - y|
Calculation:
(10x + y) - (10y + x) = 9
⇒ 10x + y - 10y - x = 9
⇒ 9x - 9y = 9
⇒ 9(x - y) = 9
⇒ x - y = 1
⇒ Difference between two digits = |x - y| = 1
∴ The correct answer is option (4).
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