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Rank after Interchange

Introduction

Rank interchange वाले questions यह पूछते हैं कि जब दो लोग लाइन में अपनी positions बदलते हैं, तो उनकी ranks कैसे बदलती हैं। यह pattern seating और ranking problems में बहुत आता है और यह टेस्ट करता है कि आप कितनी जल्दी positions को एक end से दूसरे end में convert कर सकते हैं और swap के बाद rank निकाल सकते हैं।

Conversion और swap method को समझने से mistakes नहीं होतीं, खासकर जब ranks अलग-अलग ends से दी हों या total दिया हो/न दिया हो।

Pattern: Rank after Interchange

Pattern

मुख्य concept: पहले दोनों ranks को एक ही reference (हमेशा left-end सबसे आसान) में convert करें, फिर positions swap करें, और फिर requested side से नई rank निकालें।

Useful formulas:

  • Right position = Total - Left position + 1
  • Total = Left position + Right position - 1 (जब एक ही व्यक्ति की दोनों positions दी हों)
  • Swap के बाद नई position = दूसरे व्यक्ति की पुरानी position

Step-by-Step Example

Question

20 students की row में, A left से 5th है और B right से 8th है। वे दोनों अपनी जगह बदलते हैं। Swap के बाद A की नई rank right से क्या होगी और B की नई rank left से क्या होगी?

Solution

  1. Step 1: Given positions और total लिखें

    Total = 20, A = left से 5th, B = right से 8th

  2. Step 2: B की position को left-reference में convert करें

    B from left = 20 - 8 + 1 = 13th

  3. Step 3: Swap होने वाली positions note करें

    A की old-left position = 5 B की old-left position = 13 Swap के बाद:
    • A नई left position = 13
    • B नई left position = 5

  4. Step 4: A की नई left-position को right-position में convert करें

    A from right = 20 - 13 + 1 = 8th from right

  5. Step 5: B की नई position

    B नई left-rank = 5th from left

  6. Final Answer:

    A = 8th from right; B = 5th from left

  7. Quick Check:

    A अब left 13 पर है → right = 8 सही। B अब left 5 पर है → left = 5 सही। ✅

Quick Variations

1. अगर दोनों ranks left और right दोनों से दी हों तो पहले एक ही reference में convert करके swap करें।

2. अगर total न दिया हो लेकिन किसी एक व्यक्ति की left और right rank दी हो, तो Total = left + right - 1 से निकालें।

3. Multiple swaps हों तो हर swap को step-by-step नई स्थिति मानकर करें।

4. Swap के बाद “कितने लोग बीच में हैं” पूछा जाए तो नई positions से difference formula लागू करें।

Trick to Always Use

  • Step 1 → सभी ranks को left-reference में convert करें।
  • Step 2 → Numeric positions को सीधे swap करें।
  • Step 3 → Requested side (right/top) में convert करें: Total - pos + 1।

Summary

Summary

  • Swap questions में सबसे पहले दोनों positions को एक ही end (left/top) में बदलें।
  • Right = Total - Left + 1 formula हमेशा उपयोग करें।
  • Swap के बाद हर व्यक्ति की position = दूसरे की पुरानी position।
  • Quick-check करके opposite-end rank verify करें।

याद रखने योग्य उदाहरण:
A left से 4th और B right से 3rd हों → पहले B को left में बदलें, फिर swap करें, फिर requested ranks निकालें।

Practice

(1/5)
1. In a row of 25 students, A is 7th from the left and B is 10th from the right. They interchange their positions. What is A’s new rank from the right?
easy
A. 10th from right
B. 9th from right
C. 11th from right
D. 12th from right

Solution

  1. Step 1: Write given data

    Total = 25; A = 7th from left; B = 10th from right.

  2. Step 2: Convert B’s position to left reference

    B from left = 25 - 10 + 1 = 16th from left.

  3. Step 3: After interchange

    A moves to B’s old place → left position = 16.

  4. Step 4: Convert A’s new left position to right

    A’s new right = 25 - 16 + 1 = 10th from right.

  5. Final Answer:

    10th from right → Option A

  6. Quick Check:

    Left 16 → Right = 25 - 16 + 1 = 10 ✅
Hint: Convert the given right-position to left, swap left positions, then convert back if needed.
Common Mistakes: Not converting ranks to the same reference before swapping.
2. In a line of 30 people, Rohan is 5th from the left and Sneha is 6th from the right. They interchange their positions. What is Rohan’s new rank from the left?
easy
A. 23rd from left
B. 24th from left
C. 25th from left
D. 26th from left

Solution

  1. Step 1: Convert Sneha’s rank to left reference

    Sneha from left = 30 - 6 + 1 = 25th from left.

  2. Step 2: Swap positions

    Rohan moves to Sneha’s old left position → 25th from left.

  3. Final Answer:

    25th from left → Option C

  4. Quick Check:

    Left 25 corresponds to right = 30 - 25 + 1 = 6 ✅
Hint: Convert both ranks to one end before interchanging.
Common Mistakes: Using right-side numbers directly without conversion.
3. In a row of 40 students, A is 10th from the left and B is 12th from the right. They exchange their positions. What will be B’s new rank from the right?
easy
A. 31st from right
B. 30th from right
C. 29th from right
D. 28th from right

Solution

  1. Step 1: Convert A’s position to right reference

    A from right = 40 - 10 + 1 = 31st from right.

  2. Step 2: After interchange

    B moves to A’s left position (left 10), so B’s new right = 40 - 10 + 1 = 31st from right.

  3. Final Answer:

    31st from right → Option A

  4. Quick Check:

    Left 10 → Right = 31 ✅
Hint: Swap left positions then reconvert to right as required.
Common Mistakes: Confusing old and new positions during the swap.
4. In a class of 35 students, A is 8th from the left and B is 7th from the right. If they interchange their positions, what will be A’s new rank from the right?
medium
A. 27th from right
B. 7th from right
C. 29th from right
D. 30th from right

Solution

  1. Step 1: Convert B’s right to left

    B from left = 35 - 7 + 1 = 29th from left.

  2. Step 2: Swap

    A moves to left 29 (B’s old place).

  3. Step 3: Convert to right

    A’s new right = 35 - 29 + 1 = 7th from right.

  4. Final Answer:

    7th from right → Option B

  5. Quick Check:

    Left 29 → Right = 7 ✅
Hint: Use total - left + 1 to find opposite-end position after swap.
Common Mistakes: Forgetting to add 1 while converting between ends.
5. In a queue of 50 people, P is 15th from the left and Q is 12th from the right. After they interchange their positions, what will be Q’s new rank from the left?
medium
A. 38th from left
B. 39th from left
C. 40th from left
D. 15th from left

Solution

  1. Step 1: Convert Q’s position to left

    Q from left = 50 - 12 + 1 = 39th from left.

  2. Step 2: Swap positions

    Q moves to P’s old left position → 15th from left.

  3. Final Answer:

    15th from left → Option D

  4. Quick Check:

    After swap, left 15 corresponds to right = 50 - 15 + 1 = 36 ✅
Hint: Convert to same side, swap, then reconvert if needed.
Common Mistakes: Failing to convert positions before swapping.

Mock Test

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