The sum of the digits of a two-digit number is (13). On reversing the digits, the number decreases by (45). What is the original number?

94

Let the tens digit be x and the units digit be y. Then x + y = 13. The original number is 10x + y and the reversed number is 10y + x. Using the given condition, (10x + y) − (10y + x) = 45, so 9(x − y) = 45 and x − y = 5. Solving x + y = 13 and x − y = 5 gives x = 9 and y = 4. Therefore, the original number is 94. Option 85 has a digit sum of 13, but reversing it reduces the number by only 27, so it is incorrect. Exam tip: represent a two-digit number as 10x + y and its reversal as 10y + x.

This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..