In a special arithmetic code, the symbols have changed meanings: P denotes "multiplied by", R denotes "subtracted from", S denotes "added to" and Q denotes "divided by". Which of the following coded equations is actually arithmetically true when decoded?

Introduction / Context:
This question tests understanding of coded mathematical operations. The symbols P, Q, R and S do not carry their usual meanings but are remapped to standard operators. The task is to decode each option and check which one becomes a correct arithmetic equation under the real operations.

Given Data / Assumptions:

• P means multiplied by (×).
• R means subtracted from (minus type operation).
• S means added to (+).
• Q means divided by (÷).
• We assume normal arithmetic precedence rules for × and ÷ over + and −.

Concept / Approach:
We will translate each coded option into a normal arithmetic expression by replacing the symbols with their actual operators. Then we evaluate the left hand side and check whether it equals the right hand side. The option for which the decoded equation holds true is the correct answer.

Step-by-Step Solution:
Option (a): 18 R 60 Q 15 S 2. R = subtracted from, Q = ÷, S = +. Expression is (60 − 18) ÷ 15 + 2 = 42 ÷ 15 + 2 ≈ 4.8, which is not 8. Option (b): 15 S 16 Q 2 P 4. S = +, Q = ÷, P = ×, so it becomes 15 + 16 ÷ 2 × 4. Apply precedence: 16 ÷ 2 = 8, then 8 × 4 = 32. Now 15 + 32 = 47, which matches the right hand side. Option (c): 3 P 5 R 18 Q 3. Becomes 3 × 5 subtracted from 18 ÷ 3. Even with careful interpretation, this does not simplify to 6. Option (d): 15 S 28 Q 4 P 2. Becomes 15 + 28 ÷ 4 × 2. Evaluate: 28 ÷ 4 = 7, 7 × 2 = 14, 15 + 14 = 29, not 27.

Verification / Alternative check:
We can confirm option (b) again in a compact way: 15 S 16 Q 2 P 4 → 15 + 16 ÷ 2 × 4 → 15 + 8 × 4 → 15 + 32 → 47. None of the other options evaluates to the stated value, so there is only one valid equation.

Why Other Options Are Wrong:
Option (a) evaluates to approximately 4.8, not 8. Option (c) cannot be arranged to yield 6 under the given operator meanings. Option (d) evaluates to 29 instead of 27. Therefore they all fail the correctness test.

Common Pitfalls:
Typical mistakes include ignoring operator precedence, or misinterpreting the phrase subtracted from, which reverses the order of numbers. Many learners also try to manipulate the expression manually without systematically translating each symbol first, leading to confusion.

Final Answer:
The only equation that becomes arithmetically correct after decoding is 15 S 16 Q 2 P 4 = 47.