0
0

Finding Middle Position

Introduction

कई ranking questions पूछते हैं कि पंक्ति में बीच में कौन खड़ा है या central position कौन-सी है। यह pattern महत्वपूर्ण है क्योंकि seating और ranking problems में middle-position logic बार-बार आता है।

Middle-position formula जानने से simple और composite दोनों तरह की ranking problems में समय बचता है और गलतियाँ कम होती हैं।

Pattern: Finding Middle Position

Pattern

मुख्य विचार: Middle position = (n + 1) ÷ 2, जहाँ n कुल लोगों की संख्या है।

यदि n odd है तो एक ही middle person होता है। यदि n even है तो कोई एक central person नहीं होता - दो middle positions होती हैं: n/2 और (n/2) + 1।

Step-by-Step Example

Question

ग्यारह लोग एक पंक्ति में खड़े हैं। बीच में कौन है?

Solution

  1. Step 1: कुल लोगों की संख्या पहचानें

    Total, n = 11।

  2. Step 2: Middle-position formula लागू करें

    Middle = (n + 1) ÷ 2 = (11 + 1) ÷ 2 = 12 ÷ 2 = 6।

  3. Final Answer:

    6th व्यक्ति

  4. Quick Check:

    6th व्यक्ति के दोनों ओर 5-5 लोग हैं → 5 + 1 + 5 = 11 ✅

Quick Variations

1. यदि n even हो (जैसे 12 लोग), तो middle positions 6th और 7th होंगी।

2. Circular या multi-row सेटअप में पहले उसे linear position में convert करें, फिर formula लागू करें।

3. यदि पूछा जाए “A और B के ठीक बीच में कौन है”, तो दोनों के बीच के लोग गिनें या उनकी ranks को absolute positions में बदलकर middle निकालें।

Trick to Always Use

  • Step 1 → जाँचे कि कुल n odd है या even।
  • Step 2 → Odd हो तो: middle = (n + 1) ÷ 2; Even हो तो: दो middle positions = n/2 और n/2 + 1।

Summary

Summary

  • Odd n के लिए single middle = (n + 1) ÷ 2।
  • Even n के लिए middle के दो स्थान = n/2 और (n/2) + 1।
  • हमेशा दोनों तरफ़ के लोगों को गिनकर quick check करें।
  • Composite या circular arrangements को पहले linear में बदलें।

याद रखने के लिए उदाहरण:
13 लोगों के लिए middle = (13 + 1) ÷ 2 = 7 → 7th व्यक्ति बीच में है।

Practice

(1/5)
1. In a row of 9 students, who is in the middle position?
easy
A. 4th
B. 5th
C. 6th
D. 7th

Solution

  1. Step 1: Identify total number of students

    n = 9.

  2. Step 2: Apply middle-position formula

    Middle = (n + 1) ÷ 2 = (9 + 1) ÷ 2 = 10 ÷ 2 = 5.

  3. Final Answer:

    5th position → Option B

  4. Quick Check:

    4 students before + 1 middle + 4 after = 9 ✅
Hint: Use (n + 1) ÷ 2 for odd numbers.
Common Mistakes: Using n ÷ 2 instead of (n + 1) ÷ 2 for odd totals.
2. In a line of 12 people, what are the two middle positions?
easy
A. 6th and 7th
B. 5th and 6th
C. 7th and 8th
D. 4th and 5th

Solution

  1. Step 1: Identify total people

    n = 12 (even).

  2. Step 2: Middle positions

    For even n, middles = n/2 and (n/2) + 1 = 12/2 and 12/2 + 1 = 6th and 7th.

  3. Final Answer:

    6th and 7th positions → Option A

  4. Quick Check:

    5 people before 6th and 5 after 7th → balanced ✅
Hint: For even n, use n/2 and (n/2) + 1.
Common Mistakes: Choosing only one middle position when n is even.
3. If there are 17 chairs in a row, which chair is at the center?
easy
A. 8th
B. 9th
C. 10th
D. 11th

Solution

  1. Step 1: Total chairs

    n = 17.

  2. Step 2: Apply middle formula

    Middle = (n + 1) ÷ 2 = (17 + 1) ÷ 2 = 18 ÷ 2 = 9.

  3. Final Answer:

    9th chair → Option B

  4. Quick Check:

    8 on each side → perfectly centered ✅
Hint: Middle = (n + 1) ÷ 2 when n is odd.
Common Mistakes: Dividing by 2 directly (n ÷ 2) gives wrong middle for odd totals.
4. In a line of 20 students, which two students are in the middle?
medium
A. 9th and 10th
B. 10th and 11th
C. 11th and 12th
D. 12th and 13th

Solution

  1. Step 1: Total number of students

    n = 20 (even).

  2. Step 2: Find two middle positions

    n/2 = 10, (n/2) + 1 = 11 → 10th and 11th.

  3. Final Answer:

    10th and 11th → Option B

  4. Quick Check:

    9 on each side of 10th and 11th → perfectly balanced ✅
Hint: Even n → two middle positions are n/2 and (n/2) + 1.
Common Mistakes: Picking only one middle when two exist for even totals.
5. A class has 25 students standing in a line. Which student stands exactly in the middle?
medium
A. 12th
B. 13th
C. 14th
D. 15th

Solution

  1. Step 1: Identify total students

    n = 25.

  2. Step 2: Apply middle formula

    Middle = (n + 1) ÷ 2 = (25 + 1) ÷ 2 = 26 ÷ 2 = 13.

  3. Final Answer:

    13th student → Option B

  4. Quick Check:

    12 before + 12 after = 24 others ✅
Hint: Add 1 to total, divide by 2.
Common Mistakes: Using n ÷ 2 gives wrong result for odd totals.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes