Question

The sum of a two-digit number and the number obtained by reversing the digits is 99. If the digits of the number differ by 7, then the two-digit number can be:

• A. 92
• B. 29
• C. 81
• D. 18

Hint:

Use algebraic expressions for digits and solve simultaneous equations to find digits.

Answer 1

The Correct Option is A

Let the two-digit number be \(10x + y\), where \(x\) and \(y\) are digits (with \(x > y\) or \(y > x\)).
Sum of number and reversed number: \[ (10x + y) + (10y + x) = 99 \] \[ 11(x + y) = 99 \Rightarrow x + y = 9 \] Given the digits differ by 7: \[ |x - y| = 7 \] Solve the system: Case 1: \(x - y = 7\)
From \(x + y = 9\), add both equations: \[ 2x = 16 \Rightarrow x = 8, \quad y = 1 \] Number is 81. (Option c) Case 2: \(y - x = 7\)
From \(x + y = 9\), add: \[ 2y = 16 \Rightarrow y = 8, \quad x = 1 \] Number is 18. (Option d) Thus, possible numbers are 81 and 18, both satisfying the conditions.