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Scheduling (Days/Months)

Introduction

Scheduling (Days/Months) pattern में events, people या tasks को खास days, dates या months पर assign किया जाता है और इसमें “before”, “after”, “two days after”, “in the same month as” जैसे relative-order clues का उपयोग होता है।

यह topic competitive exams (SBI PO, IBPS, SSC, CAT) में बहुत आम है और आपकी ability को test करता है कि आप temporal clues को ordered timeline में कैसे बदलते हैं।

Pattern: Scheduling (Days/Months)

Pattern

Events या persons को specific days/months पर ordering और positional constraints (before/after, immediate next, n-day gaps) के आधार पर assign किया जाता है।

  • Absolute vs Relative: Absolute clues specific dates देते हैं (जैसे 10th July); relative clues positions को compare करते हैं (जैसे X is two days after Y).
  • Immediate Relations: “Next day”, “immediately after/before” adjacency दिखाते हैं।
  • Counting Gaps: “Two days after” का मतलब दो दिन का gap (बीच में एक दिन skip)।
  • Multiple Attributes: Day/month + अन्य attributes (person, venue) का combo बड़े scheduling problems में उपयोग होता है।

Step-by-Step Example

Question

सात दोस्त - A, B, C, D, E, F और G - Monday से Sunday तक अलग-अलग days पर weekly workshops attend करते हैं। कोई दो लोग एक ही दिन नहीं जाते। Clues:
1. C, A के two days after जाता है।
2. E, D के immediately before जाता है।
3. B, Thursday को जाता है।
4. F, C के just after जाता है।
Saturday को कौन जाता है?

Options:
A) A    B) D    C) F    D) G

Solution

  1. Step 1: Map fixed day

    B = Thursday (given)।

  2. Step 2: Use relative offsets for A and C

    C = A + 2 (उदा., यदि A = Monday, तो C = Wednesday)।

  3. Step 3: F relation

    F = C + 1 (C के बाद वाला दिन)।

  4. Step 4: E-D adjacency

    E = D - 1 (adjacent pair)।

  5. Step 5: Fit around known B = Thursday

    A के positions try करें ताकि C और F, B से टकराएँ नहीं। • A = Monday → C = Wednesday → F = Thursday ❌ (B = Thursday से conflict) • A = Tuesday → C = Thursday → F = Friday ❌ (C = Thursday → फिर से conflict) • A = Wednesday → C = Friday → F = Saturday ✔ (fits perfectly)

  6. Final Answer:

    F → Option C

  7. Quick Check:

    A = Wednesday ✔ C = Friday (two days after) ✔ F = Saturday ✔ B = Thursday ✔ E-D adjacent remaining slots में fit ✔

Quick Variations

1. Weekday scheduling (Mon-Sun) + n-day gaps।

2. Monthly scheduling (Jan-Dec) + seasons/fiscal quarters।

3. Multi-attribute scheduling (day + venue + person) - tables/grids उपयोग करें।

4. Circular weekly cycles (events repeat) → modular arithmetic helpful।

Trick to Always Use

  • Step 1: Fixed days पहले रखें (जैसे B = Thursday)।
  • Step 2: Relative clues को numeric shifts में बदलें (A + 2 → C)।
  • Step 3: Adjacency blocks (E-D) को एक unit की तरह fit करें।
  • Step 4: Minimal consistent placement try करें और conflict होने पर shift करें।

Summary

Summary

  • Fixed dates/days पहले रखें, फिर relative chains (A + n → B) लगाएँ।
  • Adjacency clues को inseparable blocks की तरह treat करें।
  • Week boundaries (Mon-Sun) को याद रखें और edge cases चेक करें।
  • Initial placement के बाद conflicts चेक करें और जरूरत पर chain adjust करें।

याद रखने योग्य उदाहरण:
जब C, A के two days after है और F, C के just बाद - तो A को इस तरह रखें कि C और F किसी fixed-day (जैसे B = Thursday) से ना टकराएँ।

Practice

(1/5)
1. Five colleagues - P, Q, R, S, and T - present monthly reports in January, February, March, April, and May (one per month). The clues are: 1. P presents in January. 2. R presents immediately after P. 3. S presents in May. 4. Q presents two months after R. Who presents in April?
easy
A. T
B. P
C. Q
D. R

Solution

  1. Step 1: Fix the known positions

    P = January (given).

  2. Step 2: Apply 'immediately after' clue

    R presents immediately after P → R = February.

  3. Step 3: Apply 'two months after' clue

    Q presents two months after R → R = February, so Q = April.

  4. Step 4: Use remaining clues

    S = May (given). The remaining unassigned month is March → T = March.

  5. Step 5: Identify the target month

    The person presenting in April is Q.

  6. Final Answer:

    Q → Option C

  7. Quick Check:

    P Jan ✅ R Feb (after P) ✅ Q Apr (two after R) ✅ S May ✅ T fills March ✅
Hint: Fill fixed and immediate clues first, then apply any +n or -n month relations to deduce remaining placements.
Common Mistakes: Misinterpreting 'two months after' as skipping only one month instead of counting two months ahead.
2. Seven friends - A, B, C, D, E, F, G - attend workshops, one per weekday Monday→Sunday. Clues: 1. A attends on Monday. 2. B attends two days before D. 3. C attends immediately after B. 4. E attends on Saturday. Who attends on Thursday?
easy
A. D
B. A
C. C
D. G

Solution

  1. Step 1: Fix A and E

    A = Monday; E = Saturday.

  2. Step 2: Use B and C relation

    C is immediately after B → (B, C) are consecutive.

  3. Step 3: B two days before D

    So positions are B → C (immediate) and D is two days after B (B + 2 = D).

  4. Step 4: Try placement

    If B = Tuesday → C = Wednesday → D = Thursday. This fits with A = Monday and E = Saturday and leaves F/G for Friday/Sunday.

  5. Final Answer:

    D → Option A

  6. Quick Check:

    A Monday ✅ B Tuesday, C Wednesday, D Thursday (B two before D) ✅ E Saturday ✅
Hint: Treat 'two days before' as a +2 offset when you fix one part of the chain.
Common Mistakes: Placing B/C around fixed days and causing conflicts with the fixed weekday(s).
3. Three audits are scheduled in January, February and March for X, Y and Z. X is scheduled in February. Y is scheduled before X. Who is scheduled in January?
easy
A. Z
B. Y
C. X
D. None of the above

Solution

  1. Step 1: Fix X

    X = February (given).

  2. Step 2: Place Y before X

    Y must be scheduled earlier than X → Y = January.

  3. Step 3: Remaining assignment

    Remaining person Z = March.

  4. Final Answer:

    Y → Option B

  5. Quick Check:

    Y January ✅ X February ✅ Z March ✅
Hint: When one is fixed, use 'before/after' to place the others in earliest/latest available slots.
Common Mistakes: Assuming 'before' could mean non-consecutive without checking available months.
4. Six conferences are planned in January-June (one per month). The clues: 1. A is in March. 2. B is two months after C. 3. D is immediately before E. 4. F is in January. Which conference is in May?
medium
A. B
B. C
C. D
D. A

Solution

  1. Step 1: Fix A and F

    A = March (Mar); F = January (Jan).

  2. Step 2: Use B-C relation

    B = C + 2 (B two months after C).

  3. Step 3: D-E adjacency

    D immediately before E → (D, E) consecutive.

  4. Step 4: Construct a consistent arrangement

    Available months: Jan(F), Feb( ), Mar(A), Apr( ), May( ), Jun( ). Choose C = Feb → B = Apr. That leaves D and E to be placed as consecutive pair in May-June with D before E → D = May, E = June.

  5. Final Answer:

    D → Option C

  6. Quick Check:

    F Jan ✅ A Mar ✅ C Feb & B Apr (two months after) ✅ D May immediately before E Jun ✅
Hint: Place fixed-month items first, then slot two-month offsets and adjacent pairs into remaining months.
Common Mistakes: Assuming two-month offsets must start at the earliest month; try legal starting positions until all clues fit.
5. Seven team meetings are scheduled Monday→Sunday with one per day. Clues: 1. P is positioned between Q and R (they sit consecutively Q-P-R in that order). 2. S is two days after P. 3. T is on Sunday. 4. U is immediately before V. Who is scheduled on Tuesday?
medium
A. U
B. Q
C. P
D. V

Solution

  1. Step 1: Fix T

    T = Sunday.

  2. Step 2: Use Q-P-R block

    Q, P, R are consecutive in that order.

  3. Step 3: S is two days after P

    S = P + 2.

  4. Step 4: Place U-V adjacency

    U immediately before V → U = X, V = X + 1 (some consecutive pair).

  5. Step 5: Find a consistent placement

    Place Q = Wednesday → P = Thursday → R = Friday. Then S = Saturday and T = Sunday (fits). Remaining consecutive pair U-V take Monday-Tuesday with U = Monday and V = Tuesday. Thus Tuesday = V.

  6. Final Answer:

    V → Option D

  7. Quick Check:

    Q Wed, P Thu, R Fri ✅ S Sat (P+2) ✅ T Sun ✅ U Mon, V Tue adjacency ✅
Hint: Anchor fixed days (like T = Sunday), place multi-person blocks (Q-P-R) next, then insert adjacency pairs (U-V) into remaining earliest slots.
Common Mistakes: Forgetting to keep the order Q-P-R exact while placing S = P + 2 and T fixed.

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