Q. The sum of the digits of a two-digit number is 9. If the number formed by reversing the digits is 9 less than the original number, what is the original number?

The correct answer is (D) None of the above

Explanation:

Let’s solve the problem step by step.

Let the two-digit number be 10x + y where x is the tens digit and y is the units digit.

1. Sum of the digits is 9:
x + y = 9 (Equation 1)

2. Reversing the digits makes the number 9 less than the original:
10y + x = 10x + y – 9 (Equation 2)

Simplify Equation 2:
10y + x = 10x + y – 9
9y – 9x = -9
y – x = -1 (Equation 3)

3. Substitute Equation 3 into Equation 1:
x + (x – 1) = 9
2x – 1 = 9
2x = 10
x = 5

Then, using Equation 3:
y = x – 1 = 5 – 1 = 4

4. Original Number:
10x + y = 10(5) + 4 = 54

Checking the Options:
– (A) 27 ➔ 7 + 2 = 9 (Valid), but reversing gives 72 which is not 27 – 9 = 18
– (B) 45 ➔ 4 + 5 = 9 (Valid), but reversing gives 54 which is not 45 – 9 = 36
– (C) 63 ➔ 6 + 3 = 9 (Valid), but reversing gives 36 which is 63 – 27 ≠ 9
– (D) None of the above

Since 54 is not listed in the provided options, the correct answer is:

Answer: (D) None of the above