The sum of the digits of a two-digit number is (9). The difference between the number and the number with reversed digits is (27). What is the original number?
Answer and explanation
Correct answer: 63
Let the tens digit be \(x\) and the units digit be \(y\). Then \(x+y=9\). Taking the question to mean that the original number is 27 greater than its reversed number, \((10x+y)-(10y+x)=27\). Thus \(9(x-y)=27\), so \(x-y=3\). Solving the two equations gives \(x=6\) and \(y=3\). Therefore, the original number is \(63\). Although 54 has digit sum 9, its difference from 45 is only 9. Exam tip: represent a two-digit number as \(10x+y\) and its reverse as \(10y+x\).
Frequently asked questions
What is the correct answer to this question?
63
Why is this the correct answer?
Let the tens digit be \(x\) and the units digit be \(y\). Then \(x+y=9\). Taking the question to mean that the original number is 27 greater than its reversed number, \((10x+y)-(10y+x)=27\). Thus \(9(x-y)=27\), so \(x-y=3\). Solving the two equations gives \(x=6\) and \(y=3\). Therefore, the original number is \(63\). Although 54 has digit sum 9, its difference from 45 is only 9. Exam tip: represent a two-digit number as \(10x+y\) and its reverse as \(10y+x\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
