In a coded arithmetic expression, the following meanings are assigned to letters: A denotes added to, C denotes divided by, D denotes multiplied by and B denotes subtracted from (that is, it behaves like the minus operator). Using these meanings, evaluate 72 C 9 D 2 B 6 A 10 and find its numerical value.

Introduction / Context:
This question presents an expression where letters stand in for arithmetic operations. Instead of using the standard symbols plus, minus, multiplication and division, we are given A, B, C and D with specific meanings. Our task is to interpret the expression 72 C 9 D 2 B 6 A 10 using these definitions and evaluate it numerically. This problem checks our ability to perform substitution carefully and then apply arithmetic precedence rules correctly.

Given Data / Assumptions:

• A denotes added to, so A means plus.
• C denotes divided by, so C means division.
• D denotes multiplied by, so D means multiplication.
• B denotes subtracted from, which in this puzzle behaves effectively like the minus operator between two numbers.
• The expression is 72 C 9 D 2 B 6 A 10.
• Standard precedence rules of division and multiplication before addition and subtraction are applied after substitution.

Concept / Approach:
The first step is to replace the letters with their corresponding arithmetic operations to get an ordinary expression. After substitution, we handle division and multiplication from left to right before dealing with subtraction and addition. The phrase subtracted from can be linguistically tricky, but in the compact mathematical format used here, B is treated as a simple minus sign between the adjacent terms. Once the expression is fully translated, we can compute systematically to find the final result.

Step-by-Step Solution:
Step 1: Start from the coded expression 72 C 9 D 2 B 6 A 10. Step 2: Substitute each letter with its operation. C becomes division, D becomes multiplication, B becomes subtraction and A becomes addition. Step 3: The expression now reads 72 / 9 * 2 - 6 + 10. Step 4: Apply precedence. First compute the division: 72 / 9 = 8. Step 5: Next compute the multiplication: 8 * 2 = 16. The expression becomes 16 - 6 + 10. Step 6: Now handle subtraction and addition from left to right. First 16 - 6 = 10. Step 7: Then add 10 to get 10 + 10 = 20. Step 8: Therefore the value of 72 C 9 D 2 B 6 A 10 is 20.

Verification / Alternative check:
We can verify by rechecking each step. The replacement of C by division and D by multiplication is straightforward. The numbers 72, 9 and 2 clearly form 72 / 9 * 2, which equals 8 * 2 = 16. Subtracting 6 from 16 gives 10, and then adding 10 yields 20. There are no alternative interpretations of the operators that would be consistent with all of these steps, so the final answer is stable. A quick mental recomputation confirms 20 as the correct result.

Why Other Options Are Wrong:
Option 30 would require 72 / 9 * 2 to equal 26 before subtracting and adding, which is not correct. Option 35 and 25 similarly do not align with any correct sequence of operations using the given mapping. Option 10 might arise if someone stops after computing 16 - 6 and forgets the final addition of 10. None of these options are produced when we carefully apply the code and precedence rules; only 20 is consistent.

Common Pitfalls:
A common difficulty is misreading B as reversing the order of subtraction, reflecting the phrase subtracted from too literally and writing something like 6 - previous term. In this compact notation, however, B simply functions as a minus symbol between two consecutive terms. Another common mistake is to ignore the precedence of division and multiplication and to work strictly from left to right, which can lead to incorrect intermediate results. Writing the fully substituted expression before computing helps avoid such errors.

Final Answer:
Interpreting the coded operations correctly, the value of 72 C 9 D 2 B 6 A 10 is 20.