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 the two-digit number be 10x + y, where x and y are digits.
Sum of number and reversed number:
\[(10x + y) + (10y + x) = 99\]
\[11(x + y) = 99 ⇒ x + y = 9\]
Given the digits differ by 7:
\[|x - y| = 7\]
Case 1: x - y = 7
From x + y = 9, add both equations:
\[2x = 16 ⇒ x = 8, y = 1\]
Number is 81.
Case 2: y - x = 7
From x + y = 9, add:
\[2y = 16 ⇒ y = 8, x = 1\]
Number is 18.
Thus, possible numbers are 81 and 18, but choosing 81 as the answer.