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 C

Let a two-digit number be represented as 10x + y, where x and y are digits.
The sum of the number and its reverse is given as 99:
\[(10x + y) + (10y + x) = 99\]
Simplifying, we get \[11(x + y) = 99\], which leads to \[x + y = 9\].
The problem states that the digits differ by 7:
\[|x - y| = 7\]
This leads to two cases:
Case 1: x - y = 7
Adding this to the equation x + y = 9 results in \[2x = 16\], so x = 8 and y = 1. The number is 81.
Case 2: y - x = 7
Adding this to the equation x + y = 9 results in \[2y = 16\], so y = 8 and x = 1. The number is 18.
Therefore, the possible numbers are 81 and 18. The chosen answer is 81.