In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q − S = 2S and T = R + S + 3, then what is the value of P + R − T?

Numbers available: {4, 5, 10, 12, 15}. Condition Q − S = 2S → Q = 3S. Test S values: S=4 → Q=12 ✓ (both in set); S=5 → Q=15 ✓ (both in set). Condition T = R + S + 3. Case 1: S=4, Q=12. Remaining {5, 10, 15} for P, R, T. Test T = R + S + 3 = R + 7. If R=5, T=12 (taken). If R=10, T=17 (not in set). If R=15, T=22. No valid R. Case 2: S=5, Q=15. Remaining {4, 10, 12} for P, R, T. T = R + 5 + 3 = R + 8. If R=4, T=12 ✓ (12 in remaining). Then P=10. Check: P+R−T = 10+4−12 = 2. Hmm, this gives 2 not 1. Let me recheck case 1 more carefully: S=4, Q=12, remaining {5,10,15}. T = R + 4 + 3 = R + 7. If R=5, T=12 (taken, not allowed); If R=10, T=17 (not in set); if R=15, T=22 (not in set). No valid. Case 2 only: P+R−T = 10+4−12 = 2. So the answer is 2, matching option (b). The official key indicates (a) 1 in some sources; however the computation gives 2. Going with the computed answer (b) 2.