An e-commerce company has six orders – A, B, C, D, E and F – to be delivered on a particular day in a residential complex. The day has six one-hour delivery slots: 9–10, 10–11, 11–12 and 12–1 in the morning session, and 2–3 and 3–4 after the lunch break. Exactly one order is delivered in each slot. Each order is delivered by one of two agents, Ravi or Sunil, and each agent delivers exactly three orders.
The following facts are known:
1. Ravi delivers both the first order and the last order of the day.
2. B is delivered after A, with exactly one slot between the slots of A and B.
3. E is delivered by the same agent who delivers B, and E is delivered later than B.
4. C is delivered by Ravi after the lunch break.
5. F is delivered by Ravi, earlier than B.
6. D is not delivered by Sunil, and D is delivered earlier than every order that Sunil delivers.
The following facts are known:
1. Ravi delivers both the first order and the last order of the day.
2. B is delivered after A, with exactly one slot between the slots of A and B.
3. E is delivered by the same agent who delivers B, and E is delivered later than B.
4. C is delivered by Ravi after the lunch break.
5. F is delivered by Ravi, earlier than B.
6. D is not delivered by Sunil, and D is delivered earlier than every order that Sunil delivers.
Question 1
Single correct option
Which order is delivered in the 11–12 slot?
- A. A
- B. F
- C. D
- D. B
Show answer and solution
Answer: (B) F
Deduction (number the slots 1–6):
- Ravi has slots 1 and 6 (clause 1) and also delivers C, F and D (clauses 4, 5, 6). Since he delivers only three orders, these are exactly C, F, D, and Sunil delivers A, B, E.
- C is after lunch and Ravi's, so C is in slot 6 (slot 5 would give Ravi a fourth order). F or D is in slot 1.
- E comes after B and must be in slot 5 at the latest; with B two slots after A: (A, B) = (2, 4) and E = 5 [(3, 5) leaves no slot for E].
- Slot 3 then goes to Ravi. D must precede A (slot 2), so D = 1 and F = 3.
| Slot | 9–10 | 10–11 | 11–12 | 12–1 | 2–3 | 3–4 |
|---|---|---|---|---|---|---|
| Order | D | A | F | B | E | C |
| Agent | Ravi | Sunil | Ravi | Sunil | Sunil | Ravi |
(If F were first, D would come after Sunil's A, violating clause 6.) So F is in 11–12.
- Ravi has slots 1 and 6 (clause 1) and also delivers C, F and D (clauses 4, 5, 6). Since he delivers only three orders, these are exactly C, F, D, and Sunil delivers A, B, E.
- C is after lunch and Ravi's, so C is in slot 6 (slot 5 would give Ravi a fourth order). F or D is in slot 1.
- E comes after B and must be in slot 5 at the latest; with B two slots after A: (A, B) = (2, 4) and E = 5 [(3, 5) leaves no slot for E].
- Slot 3 then goes to Ravi. D must precede A (slot 2), so D = 1 and F = 3.
| Slot | 9–10 | 10–11 | 11–12 | 12–1 | 2–3 | 3–4 |
|---|---|---|---|---|---|---|
| Order | D | A | F | B | E | C |
| Agent | Ravi | Sunil | Ravi | Sunil | Sunil | Ravi |
(If F were first, D would come after Sunil's A, violating clause 6.) So F is in 11–12.
Question 2
Numerical answer
How many orders are delivered after A but before C?
Show answer and solution
Answer: 3
Deduction (number the slots 1–6):
- Ravi has slots 1 and 6 (clause 1) and also delivers C, F and D (clauses 4, 5, 6). Since he delivers only three orders, these are exactly C, F, D, and Sunil delivers A, B, E.
- C is after lunch and Ravi's, so C is in slot 6 (slot 5 would give Ravi a fourth order). F or D is in slot 1.
- E comes after B and must be in slot 5 at the latest; with B two slots after A: (A, B) = (2, 4) and E = 5 [(3, 5) leaves no slot for E].
- Slot 3 then goes to Ravi. D must precede A (slot 2), so D = 1 and F = 3.
| Slot | 9–10 | 10–11 | 11–12 | 12–1 | 2–3 | 3–4 |
|---|---|---|---|---|---|---|
| Order | D | A | F | B | E | C |
| Agent | Ravi | Sunil | Ravi | Sunil | Sunil | Ravi |
A is at 10–11 and C at 3–4; the orders between them are F, B and E → 3.
- Ravi has slots 1 and 6 (clause 1) and also delivers C, F and D (clauses 4, 5, 6). Since he delivers only three orders, these are exactly C, F, D, and Sunil delivers A, B, E.
- C is after lunch and Ravi's, so C is in slot 6 (slot 5 would give Ravi a fourth order). F or D is in slot 1.
- E comes after B and must be in slot 5 at the latest; with B two slots after A: (A, B) = (2, 4) and E = 5 [(3, 5) leaves no slot for E].
- Slot 3 then goes to Ravi. D must precede A (slot 2), so D = 1 and F = 3.
| Slot | 9–10 | 10–11 | 11–12 | 12–1 | 2–3 | 3–4 |
|---|---|---|---|---|---|---|
| Order | D | A | F | B | E | C |
| Agent | Ravi | Sunil | Ravi | Sunil | Sunil | Ravi |
A is at 10–11 and C at 3–4; the orders between them are F, B and E → 3.
Question 3
Single correct option
Which of the following pairs of orders are delivered by the same agent?
- A. D and B
- B. F and E
- C. C and A
- D. A and E
Show answer and solution
Answer: (D) A and E
Deduction (number the slots 1–6):
- Ravi has slots 1 and 6 (clause 1) and also delivers C, F and D (clauses 4, 5, 6). Since he delivers only three orders, these are exactly C, F, D, and Sunil delivers A, B, E.
- C is after lunch and Ravi's, so C is in slot 6 (slot 5 would give Ravi a fourth order). F or D is in slot 1.
- E comes after B and must be in slot 5 at the latest; with B two slots after A: (A, B) = (2, 4) and E = 5 [(3, 5) leaves no slot for E].
- Slot 3 then goes to Ravi. D must precede A (slot 2), so D = 1 and F = 3.
| Slot | 9–10 | 10–11 | 11–12 | 12–1 | 2–3 | 3–4 |
|---|---|---|---|---|---|---|
| Order | D | A | F | B | E | C |
| Agent | Ravi | Sunil | Ravi | Sunil | Sunil | Ravi |
Sunil delivers A, B, E; Ravi delivers D, F, C. Only A and E share an agent.
- Ravi has slots 1 and 6 (clause 1) and also delivers C, F and D (clauses 4, 5, 6). Since he delivers only three orders, these are exactly C, F, D, and Sunil delivers A, B, E.
- C is after lunch and Ravi's, so C is in slot 6 (slot 5 would give Ravi a fourth order). F or D is in slot 1.
- E comes after B and must be in slot 5 at the latest; with B two slots after A: (A, B) = (2, 4) and E = 5 [(3, 5) leaves no slot for E].
- Slot 3 then goes to Ravi. D must precede A (slot 2), so D = 1 and F = 3.
| Slot | 9–10 | 10–11 | 11–12 | 12–1 | 2–3 | 3–4 |
|---|---|---|---|---|---|---|
| Order | D | A | F | B | E | C |
| Agent | Ravi | Sunil | Ravi | Sunil | Sunil | Ravi |
Sunil delivers A, B, E; Ravi delivers D, F, C. Only A and E share an agent.
Question 4
Numerical answer
Suppose condition 2 is replaced by: 'B is delivered at some time after A' (any number of slots may separate them), all other conditions remaining unchanged. How many different complete schedules (order and agent for every slot) would then be possible?
Show answer and solution
Answer: 3
The other conditions still force: C at 3–4 (Ravi), E at 2–3 (Sunil, same agent as B and after B), Ravi = {C, D, F}, Sunil = {A, B, E}, B at 12–1 (B must precede E and follow A and F, and B cannot be later than 12–1).
So slots 9–10, 10–11, 11–12 hold D, F and A in some order, with A before B automatically. Constraints: slot 9–10 is Ravi's (D or F), and D precedes A.
- D, A, F ✓
- D, F, A ✓
- F, D, A ✓
- F, A, D ✗ (D after A)
- A first ✗ (first slot must be Ravi's)
Hence 3 schedules.
So slots 9–10, 10–11, 11–12 hold D, F and A in some order, with A before B automatically. Constraints: slot 9–10 is Ravi's (D or F), and D precedes A.
- D, A, F ✓
- D, F, A ✓
- F, D, A ✓
- F, A, D ✗ (D after A)
- A first ✗ (first slot must be Ravi's)
Hence 3 schedules.
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