Given relations: $P = 3 \cdot T$, $T

eq 0$$S = Q + 4$$Q = R + 3$ All five digits P, Q, R, S, T are distinct and each is a single digit 0–9.

Step 1 — Possible values for T and P: Since P = 3T must be a single digit, T can be 1, 2, or 3:

• T = 1 → P = 3
• T = 2 → P = 6
• T = 3 → P = 9

Step 2 — Possible values for Q, R, S: From Q = R + 3 and S = Q + 4, Q must satisfy $0 \le R \le 9$ and $S \le 9$. Thus $R = Q - 3 \ge 0 \rightarrow Q \ge 3$. $S = Q + 4 \le 9 \rightarrow Q \le 5$. So $Q \in \{3, 4, 5\}$, giving:

• Q = 3 → R = 0, S = 7
• Q = 4 → R = 1, S = 8
• Q = 5 → R = 2, S = 9

Step 3 — Test combinations and ensure all digits are distinct: Try each (T,P) with each (Q,R,S):

T = 1, P = 3:

• Q = 3 → digits {P,Q,R,S,T} = {3,3,0,7,1} → P and Q both 3 → invalid.
• Q = 4 → digits {3,4,1,8,1} → R = 1 and T = 1 → duplicate → invalid.
• Q = 5 → digits {3,5,2,9,1} → all distinct → valid → 35291

T = 2, P = 6:

• Q = 3 → digits {6,3,0,7,2} → all distinct → valid → 63072
• Q = 4 → digits {6,4,1,8,2} → all distinct → valid → 64182
• Q = 5 → digits {6,5,2,9,2} → R = 2 and T = 2 → duplicate → invalid

T = 3, P = 9:

• Q = 3 → digits {9,3,0,7,3} → Q = 3 and T = 3 → duplicate → invalid
• Q = 4 → digits {9,4,1,8,3} → all distinct → valid → 94183
• Q = 5 → digits {9,5,2,9,3} → P = 9 and S = 9 → duplicate → invalid

Step 4 — Count valid numbers: Valid 5-digit numbers found: 35291, 63072, 64182, 94183 → total = 4.

Therefore the correct choice is (b) 4.