If "P" denotes "multiplied by", "R" denotes "subtracted", "S" denotes "added to" and "Q" denotes "divided by", then what is the value of 6 P 7 S 169 Q 13 R 5 under normal arithmetic precedence?

Introduction:
This question is based on coded arithmetic operations similar to earlier ones, where letters stand in place of conventional operators. We are required to decode the expression 6 P 7 S 169 Q 13 R 5 into standard arithmetic form and then compute its numerical value. Understanding how to map each symbol and then correctly apply precedence is essential.

Given Data / Assumptions:
We are given that P means multiplication, R means subtraction, S means addition, and Q means division. The expression to evaluate is 6 P 7 S 169 Q 13 R 5. We assume that multiplication and division are done before addition and subtraction, and we treat R as the simple minus operator between numbers in sequence.

Concept / Approach:
The approach is straight: substitute each coded symbol with its corresponding arithmetic operator to obtain a conventional expression. After that, apply BODMAS or PEMDAS rules. The most common places to make mistakes are in misreading the mapping or in ignoring operator precedence because of the unfamiliar notation.

Step-by-Step Solution:
Step 1: Substitute the operators. P is multiplication, S is addition, Q is division, and R is subtraction.Step 2: The coded expression 6 P 7 S 169 Q 13 R 5 becomes 6 * 7 + 169 / 13 - 5.Step 3: Apply precedence rules. First resolve multiplication and division from left to right.Step 4: Compute 6 * 7 = 42.Step 5: Compute 169 / 13. Since 13 * 13 = 169, we get 169 / 13 = 13.Step 6: Substitute these values into the expression: it becomes 42 + 13 - 5.Step 7: Now perform the addition and subtraction from left to right. First, 42 + 13 = 55.Step 8: Then subtract 5: 55 - 5 = 50.Step 9: Therefore, the value of the expression is 50.

Verification / Alternative check:
Recomputing quickly, 6 times 7 is 42, adding 13 gives 55, and subtracting 5 yields 50. There are no conflicting interpretations if the mappings are applied as given, so the result is stable.

Why Other Options Are Wrong:
The value 55 would occur if someone ignored the final subtraction and stopped after 42 + 13. The value 45 might result from incorrectly subtracting 10 rather than 5. The value 43 and 41 do not follow from any consistent misapplication of precedence independent of gross errors in the arithmetic or mapping, so they are implausible.

Common Pitfalls:
Students sometimes reverse the roles of addition and subtraction or confuse which letter maps to which operation. Another error is to evaluate the expression strictly from left to right without respecting that multiplication and division must be resolved before addition and subtraction. Translating the expression clearly before computing helps avoid these problems.

Final Answer:
The numerical value of the expression is 50.