If P denotes '+', Q means '÷', R means '−' and S means '×', then which of the following equations is correct?

Question

If P denotes '+', Q means '÷', R means '−' and S means '×', then which of the following equations is correct?

1. A. 16 P 5 R 10 S 4 Q 3 = 19
2. B. 16 S 5 R 10 P 4 Q 3 = 9
3. C. 16 S 5 Q 10 P 4 R 3 = 9 (Correct answer)
4. D. 16 Q 5 P 10 S 4 R 3 = 12

Correct Answer

Option C — 16 S 5 Q 10 P 4 R 3 = 9

Detailed Solution & Explanation

The correct answer is 16 S 5 Q 10 P 4 R 3 = 9.

Key Points

• Substitute throughout: P = +, Q = ÷, R = −, S = ×, then evaluate each option under BODMAS.
• Option C becomes 16 × 5 ÷ 10 + 4 − 3:
  • 16 × 5 = 80, then 80 ÷ 10 = 8
  • 8 + 4 = 12, then 12 − 3 = 9 ✓ matching the stated result
• The others fail: A gives about 7.67 against a claimed 19, B gives about 71.33 against 9, and D gives 40.2 against 12.

Additional Information

• With four options to test, convert and evaluate each in full rather than trying to reason toward the answer — it is quicker and leaves no doubt.
• Division and multiplication share a precedence level and resolve left to right, so 16 × 5 ÷ 10 is (16 × 5) ÷ 10, not 16 × (5 ÷ 10).
• A quick filter: if an option produces a fraction where the stated result is a whole number, it can be discarded without finishing the arithmetic.
• Writing the converted expression above each option keeps the four evaluations separate; doing them mentally is where marks are lost.