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Order and Ranking Puzzle

Introduction

Order and Ranking Puzzles उन समस्याओं से संबंधित हैं जिनमें लोगों या वस्तुओं को उनकी positions, scores, heights या किसी अन्य measurable attribute के अनुसार arrange करना होता है। ये प्रश्न logical ordering और positional reasoning skills की परीक्षा लेने के लिए competitive exams में बहुत सामान्य होते हैं।

आपसे पूछा जा सकता है कि ऊपर से या नीचे से rank क्या है, कुल कितने लोग हैं, या दो ranks के बीच कौन है - इन सभी में consistent logic approach की आवश्यकता होती है।

Pattern: Order and Ranking Puzzle

Pattern

मुख्य विचार यह है कि दिए गए positional data को एक visual sequence में बदलें और missing rank, कुल गिनती, या दोनों सिरों के बीच की position के लिए उपयुक्त formulas लागू करें।

सामान्य clue प्रकार में शामिल हैं: 1️⃣ “A is 6th from the top, B is 10th from the bottom in a class of 20.” 2️⃣ “Find how many students are between A and B.” 3️⃣ “Find total number of students in the group.”

Step-by-Step Example

Question

एक row में A top से 8वाँ है और नीचे से 13वाँ है। उस row में कुल कितने students हैं?

विकल्प:

  • A) 19
  • B) 20
  • C) 21
  • D) 22

Solution

  1. Step 1: rank-sum संबंध का उपयोग करें

    कुल छात्रों की संख्या = (Rank from top + Rank from bottom - 1)।

  2. Step 2: मान डालें

    कुल = 8 + 13 - 1 = 20.

  3. Final Answer:

    20 → विकल्प B

  4. Quick Check:

    अगर A top से 8वाँ और bottom से 13वाँ है तो ऊपर 7 और नीचे 12 → कुल = 20 ✅

Quick Variations

1️⃣ दोनों top और bottom ranks का उपयोग करके कुल व्यक्तियों की संख्या निकालना।

2️⃣ कुल और एक तरफ के rank दिए हों तो दूसरी तरफ का rank निकालना।

3️⃣ दो ranks के बीच आने वाले लोगों की संख्या निकालना।

4️⃣ तुलना-प्रकार (उदा., A is 3rd taller than B) की समस्याएँ।

Trick to Always Use

  • Step 1: भ्रम से बचने के लिए एक visual number line बनाएं (Top → Bottom)।
  • Step 2: सार्वभौमिक सूत्र का उपयोग करें: कुल = (Rank from Top + Rank from Bottom - 1).
  • Step 3: “दो व्यक्तियों के बीच” के लिए उपयोग करें: Difference - 1.
  • Step 4: सुनिश्चित करें कि rank directions (top/bottom या left/right) consistent हैं।

Summary

Summary

  • Rank clues को numeric equations या sequences में बदलें।
  • कुल गिनती निकालने के लिए core rank-sum formula का उपयोग करें।
  • विपरीत सिरों से rank निकालने के लिए उपयोग करें: Rank from bottom = Total - Rank from top + 1.
  • गलत reversal errors से बचने के लिए छोटे उदाहरणों से sequence visualize करें।

याद रखने योग्य उदाहरण:
यदि कोई छात्र top से 7वाँ और bottom से 14वाँ है, तो कुल = 7 + 14 - 1 = 20 students।

Practice

(1/5)
1. In a row of students, X is 5th from the top and 12th from the bottom. How many students are there in the row?
easy
A. 16
B. 17
C. 18
D. 19

Solution

  1. Step 1: Use the rank-sum formula

    Total = (Rank from top + Rank from bottom - 1).

  2. Step 2: Substitute values

    Total = 5 + 12 - 1 = 16.

  3. Final Answer:

    16 → Option A

  4. Quick Check:

    If there are 16 students, X is 5th from top → 4 above and 11 below → 12th from bottom ✅
Hint: Always apply Total = (top rank + bottom rank - 1) for direct rank pairs.
Common Mistakes: Forgetting to subtract 1 when adding ranks from both ends.
2. In a line of 30 students, A is 7th from the top and B is 3rd from the top. How many students sit between A and B?
easy
A. 3
B. 4
C. 5
D. 6

Solution

  1. Step 1: Identify positions from the same end

    A is 7th from top, B is 3rd from top (B is above A).

  2. Step 2: Calculate students between

    Positions: B at 3, then 4, 5, 6, A at 7 → students at positions 4, 5, 6 → 3 students.

  3. Step 3: Use the formula

    Number between = |7 - 3| - 1 = 4 - 1 = 3.

  4. Final Answer:

    3 → Option A
Hint: When both ranks are from the same end, use |rank1 - rank2| - 1.
Common Mistakes: Forgetting to subtract 1, which counts the endpoints themselves.
3. There are 25 candidates. C is 9th from the top. What is C’s rank from the bottom?
easy
A. 15th
B. 16th
C. 17th
D. 18th

Solution

  1. Step 1: Use conversion formula

    Rank from bottom = Total - Rank from top + 1.

  2. Step 2: Substitute values

    Rank from bottom = 25 - 9 + 1 = 17 → 17th.

  3. Final Answer:

    17th → Option C

  4. Quick Check:

    If C is 9th from top, there are 8 above and 25 - 9 = 16 below → rank from bottom = 16 + 1 = 17 ✅
Hint: Always use Total - topRank + 1 to convert ranks between ends.
Common Mistakes: Forgetting the +1 when converting ranks.
4. In a row, A is 11th from the top and B is 17th from the bottom. If A is above B and there are 4 students between them, how many students are in the row?
medium
A. 28
B. 29
C. 30
D. 32

Solution

  1. Step 1: Let total = T and convert B’s top rank

    B from top = T - 17 + 1 = T - 16.

  2. Step 2: Use the gap relation (A above B)

    Number between = (top rank of lower person) - (top rank of higher person) - 1. So (T - 16) - 11 - 1 = 4 ⇒ T - 28 = 4.

  3. Step 3: Solve for T

    T = 32.

  4. Step 4: Verify the original clues

    If T = 32, B from top = 32 - 16 = 16, so positions are A = 11 and B = 16 → people between = 12,13,14,15 = 4. Also B from bottom = 32 - 16 + 1 = 17 → matches given '17th from the bottom'.

  5. Final Answer:

    32 → Option D

  6. Quick Check:

    T = 32 ✅ A at 11th from top ✅ B at 16th from top which is 17th from bottom ✅ exactly 4 between (12-15) ✅
Hint: Convert the bottom-given rank to its top-rank expression (T - bottom + 1), then use (difference - 1) = number between to solve for T.
Common Mistakes: Forgetting the -1 in the 'between' formula or failing to explicitly re-check the bottom-given rank after solving for T.
5. In a row, X is 14th from the left and Y is 20th from the left. There are 5 people between X and Y. If X is to the left of Y, how many people are there in the row (minimum consistent total)?
medium
A. 20
B. 21
C. 22
D. 23

Solution

  1. Step 1: Both ranks given from left

    X = 14th, Y = 20th.

  2. Step 2: Verify the number between

    Number between = |20 - 14| - 1 = 6 - 1 = 5 → matches given data.

  3. Step 3: Determine minimal total

    The highest given position is 20 (Y). If no person is specified after Y, the minimal consistent total = 20.

  4. Final Answer:

    20 → Option A
Hint: When both ranks are from same side, the maximum rank given is a lower bound for total; verify gaps first, then decide if additional people after the higher rank are required.
Common Mistakes: Adding the 'between' people again to the higher rank (double-counting).

Mock Test

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