In a coded arithmetic expression, "S" denotes "multiplied by", "P" denotes "subtracted from", "R" denotes "added to" and "Q" denotes "divided by". Using these operator codes, what is the numerical value of 14641 Q 121 P 100 S 2 R 100 ?

Introduction / Context:
This coding and decoding problem tests understanding of how familiar arithmetic operators are replaced by symbolic letters and how to correctly substitute and evaluate a compound expression. Many competitive exams use such questions to check whether candidates follow operator meaning and precedence rules carefully rather than performing operations mechanically.

Given Data / Assumptions:

• "S" denotes multiplication.
• "P" denotes subtraction.
• "R" denotes addition.
• "Q" denotes division.
• Expression to evaluate: 14641 Q 121 P 100 S 2 R 100.
• Standard arithmetic precedence applies: division and multiplication before addition and subtraction, and evaluation is from left to right within the same precedence level.

Concept / Approach:
The key idea is to translate each coded symbol back to the usual arithmetic operator and then compute the value step by step. Once the operators are decoded, we must apply the normal BODMAS or PEMDAS rule, giving priority to division and multiplication over addition and subtraction. Although the text uses the phrase "subtracted from" for P, in this common exam pattern P simply acts as the minus operator between left and right operands after decoding.

Step-by-Step Solution:
Step 1: Replace each coded symbol with its corresponding arithmetic operator. 14641 Q 121 P 100 S 2 R 100 becomes 14641 ÷ 121 - 100 × 2 + 100. Step 2: Apply operator precedence and first handle the division 14641 ÷ 121. Step 3: 14641 is 121 squared, so 14641 ÷ 121 = 121. Step 4: Now evaluate the multiplication 100 × 2 = 200. Step 5: After these operations, the expression becomes 121 - 200 + 100. Step 6: Now perform subtraction and addition from left to right: first compute 121 - 200 = -79. Step 7: Add 100 to the result: -79 + 100 = 21. Step 8: Therefore, the numerical value represented by the coded expression is 21.

Verification / Alternative check:
We can quickly verify by recomputing in a compact way. Once decoded, the expression is 14641 ÷ 121 - 100 × 2 + 100. Since 14641 ÷ 121 = 121 and 100 × 2 = 200, we obtain 121 - 200 + 100. Grouping the last two terms as -200 + 100 = -100 gives 121 - 100 = 21. This independent recomputation confirms that 21 is correct, so there is no arithmetic mistake in the stepwise solution.

Why Other Options Are Wrong:
Option 48 would arise if division and multiplication precedence were ignored or misapplied. Option 61 and option 31 typically come from doing the operations strictly left to right without respecting that multiplication and division should be performed before addition and subtraction. Another incorrect value can appear if a candidate misinterprets P and changes operand order, but with the standard exam convention used here, such an interpretation is not intended. Hence these options are distractors based on common calculation errors.

Common Pitfalls:
A frequent mistake is to replace the coded symbols correctly but then apply operations strictly from left to right, which violates operator precedence rules. Another common trap is overthinking the phrase "subtracted from" and reversing the order of subtraction, even though such questions usually expect candidates to treat P as the normal minus sign once decoded. Errors in observing that 14641 equals 121 squared can also introduce division mistakes. Working carefully and simplifying each part systematically prevents these issues and leads to the correct answer.

Final Answer:
After decoding each symbol and evaluating using correct arithmetic precedence, the coded expression 14641 Q 121 P 100 S 2 R 100 is equal to 21, so the correct option is 21.