Select the correct alternative from the given choices. The...

Select the correct alternative from the given choices.
The digits of a two digit number differ by 3 . Find the difference of the number and the number formed by reversing its digits.
(A) 18
(B) 27
(C) 36
(D) 45

Key Concepts

Difference Between a Number and Its Reversal

Subtracting the number formed by reversing the digits from the original number reveals a pattern in how the digits contribute to its overall value. Algebraically, this difference can often be expressed in terms of a multiple of the difference between the individual digits, which underscores its dependency on digit positions.

Properties of Multiples of Nine

The operation of subtracting the reversed number from the original number leads to a result that is a multiple of nine. This is due to the specific structure of the base-10 system, where the difference between the two representations factors into 9 times the difference between the digits.

Digit Reversal

Reversing the digits of a number involves interchanging the tens and the units digits. Understanding how this operation changes the value of a number is crucial to establishing relationships between the original and the reversed number.

Place Value System

The place value system allows any number, particularly a two-digit number, to be expressed in terms of its individual digits multiplied by their corresponding weights (for example, tens and units). This concept is essential for breaking down numbers into components that can be manipulated algebraically.

Algebraic Representation of Numbers

Representing a number algebraically by denoting its digits as variables (such as 'a' for the tens digit and 'b' for the units digit) provides a general framework for solving problems. This technique enables derivation of relationships and formulas that are independent of specific numerical instances.

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