In a certain coded arithmetic system, the usual meanings of the symbols are changed as follows: the symbol - means division, the symbol + means multiplication, the symbol ÷ means subtraction and the symbol x means addition. Which one of the following equations becomes numerically correct when the given meanings of the symbols are applied?

Introduction / Context:
This problem is a typical example of coded arithmetic, where familiar mathematical symbols are assigned new meanings. Instead of performing the operations as they appear, we need to carefully replace each symbol with its new meaning and then evaluate the equation. The goal is to identify which option gives a true numerical statement after applying the code. This tests accuracy in symbol substitution, understanding of operation precedence and basic arithmetic skills under a small twist.

Given Data / Assumptions:

• The symbol - means division.
• The symbol + means multiplication.
• The symbol ÷ means subtraction.
• The symbol x means addition.
• We must apply normal arithmetic precedence for multiplication, division, addition and subtraction after substitution.
• We need to find the option where the left side equals the right side under these coded meanings.

Concept / Approach:
The key idea is to treat each expression as a coded string where every operator symbol must be translated into its true arithmetic meaning. Once that translation is done, we obtain an ordinary arithmetic expression that we can evaluate using standard precedence rules, performing multiplication and division before addition and subtraction. We repeat this procedure for each option until we find the equation that balances correctly. It is important to avoid casual mental substitution and to work systematically to prevent small mistakes from flipping the result.

Step-by-Step Solution:
Step 1: Focus on option B: 48 ÷ 5 + 8 x 10 - 2 = 13. Step 2: Substitute each symbol using the code. ÷ means subtraction, + means multiplication and x means addition, while - means division. Step 3: After substitution, the left side becomes 48 - 5 * 8 + 10 / 2. Step 4: Apply precedence. First multiply and divide: 5 * 8 = 40 and 10 / 2 = 5. Step 5: Now the expression is 48 - 40 + 5. Step 6: Perform subtraction and addition from left to right: 48 - 40 = 8, then 8 + 5 = 13. Step 7: The left side equals 13, which matches the right side, so option B becomes a correct equation under the coded rules.

Verification / Alternative check:
To ensure that option B is uniquely correct, we can briefly inspect the other options. For example, in option A the substituted expression does not simplify to 25, and in options C and D the resulting values are very different from the stated right side numbers. You can verify this by performing the same substitution and evaluation procedure, and you will see that none of them balance exactly. Therefore, only option B satisfies the coded arithmetic system. This confirms that our substitution method and calculation steps are correct.

Why Other Options Are Wrong:
In option A, when the operators are replaced with their true meanings, the left side evaluates to a value not equal to 25. Similarly, in option C, after substitution the operations give a result far from 420. Option D also fails when evaluated correctly; its left side does not equal 28. Option E is an additional distractor and likewise does not produce equality after applying the code and standard precedence. These options are designed to catch candidates who misapply the symbol meanings or perform operations in the wrong order.

Common Pitfalls:
A common mistake is to forget that the original symbols no longer have their usual meanings and to calculate them directly as seen. Another frequent error is ignoring the precedence rules after substitution and simply operating from left to right. Some test takers also misread the mapping for one symbol, such as treating ÷ as division instead of subtraction in this particular code. Carefully rewriting the coded expression into a normal arithmetic form before computing greatly reduces these errors and leads to a reliable answer.

Final Answer:
The only equation that becomes numerically correct when the given coded meanings of the symbols are applied is 48 ÷ 5 + 8 x 10 - 2 = 13.