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Combined Rank from Two Lists

Introduction

कई ranking problems में किसी व्यक्ति की position top (या left) से और bottom (या right) से दी होती है। इन दोनों references को जल्दी और सही तरीके से convert करना aptitude में बहुत महत्वपूर्ण है।

यह pattern इसलिए जरूरी है क्योंकि किसी एक व्यक्ति की top और bottom ranks मिल जाएँ, तो total size तुरंत मिल जाता है - और उसी से कई तरह के follow-up questions आसानी से हल हो जाते हैं।

Pattern: Combined Rank from Two Lists

Pattern

मुख्य concept: Total = (Rank from top) + (Rank from bottom) - 1

Derived useful formulas:

  • अगर कोई व्यक्ति rtop top से और rbottom bottom से है → total n = rtop + rbottom - 1
  • अगर total n और एक side की rank दी हो → opposite rank = n - given + 1
  • अगर दो व्यक्तियों की ranks opposite ends से दी हों → पहले दोनों को एक ही reference (top) में convert करें और फिर difference formulas लगाएँ

Step-by-Step Example

Question

Anu class में top से 7th है और bottom से 18th है। Class में total students कितने हैं?

Solution

  1. Step 1: दिए गए ranks लिखें

    Top rank = 7, Bottom rank = 18

  2. Step 2: Combined-rank formula लगाएँ

    Total = 7 + 18 - 1 = 24

  3. Step 3: Quick verification

    Bottom rank check: 24 - 7 + 1 = 18 → दिया हुआ bottom rank match करता है।

  4. Final Answer:

    24 students

  5. Quick Check:

    6 ahead + 1 (Anu) + 17 below = 24 ✅

Quick Variations

1. एक side की rank और total दिया हो → दूसरी side की rank = n - given + 1

2. दो लोगों की ranks opposite ends से हों → दोनों को top reference में convert करके between-count निकालें

3. अगर additions/removals हों → पहले total update करें और फिर conversion लगाएँ

4. किसी X (rtop) और Y (rbottom) के बीच कितने लोग हैं → पहले Y को top में बदलें, फिर |rY_top - rX| - 1 लगाएँ

Trick to Always Use

  • Step 1: Top + Bottom - 1 से total तुरंत निकालें।
  • Step 2: Intermediate steps में rank को people-ahead (rank - 1) में बदलना आसान रहता है।
  • Step 3: दो व्यक्तियों के बीच count निकालना हो तो दोनों ranks एक ही reference पर लाएँ।

Summary

Summary

  • Total = top rank + bottom rank - 1
  • Intermediate logic के लिए ranks को people-ahead में बदलना helpful है।
  • Side-switch: opposite rank = n - given rank + 1
  • Mixed-end ranks वाले questions में दोनों ranks को पहले एक ही end पर convert करें।

Example to remember:
अगर कोई top से 5th और bottom से 12th है → total = 5 + 12 - 1 = 16 students

Practice

(1/5)
1. In a class, Rohan is 8th from the top and 13th from the bottom. Find the total number of students in the class.
easy
A. 20
B. 19
C. 21
D. 22

Solution

  1. Step 1: Write ranks

    Rank from top = 8, Rank from bottom = 13.

  2. Step 2: Apply formula

    Total = Top + Bottom - 1 = 8 + 13 - 1 = 20.

  3. Final Answer:

    20 students → Option A

  4. Quick Check:

    20 - 8 + 1 = 13 (matches bottom rank) ✅
Hint: Total = Top + Bottom - 1.
Common Mistakes: Adding both ranks without subtracting 1.
2. In a competition, Asha is 5th from the top and 22nd from the bottom. How many participants were there in total?
easy
A. 26
B. 25
C. 27
D. 28

Solution

  1. Step 1: Use combined formula

    Total = Top + Bottom - 1 = 5 + 22 - 1 = 26.

  2. Step 2: Verify

    Opposite check → 26 - 5 + 1 = 22 ✅

  3. Final Answer:

    26 participants → Option A

  4. Quick Check:

    Top + Bottom - 1 = 26 ✅
Hint: Use top + bottom - 1 formula directly.
Common Mistakes: Forgetting to subtract 1 from the total.
3. In a list of students, Priya is 9th from the top and 7th from the bottom. What is the total number of students?
easy
A. 16
B. 17
C. 15
D. 18

Solution

  1. Step 1: Apply formula

    Total = Top + Bottom - 1 = 9 + 7 - 1 = 15.

  2. Step 2: Verify

    15 - 9 + 1 = 7 → matches bottom rank.

  3. Final Answer:

    15 students → Option C

  4. Quick Check:

    Sum - 1 = 15 ✅
Hint: Always subtract 1 after adding ranks.
Common Mistakes: Including both ends without subtracting 1.
4. In a race, Ravi’s position is 10th from the start and 16th from the end. How many runners are there?
medium
A. 24
B. 23
C. 25
D. 26

Solution

  1. Step 1: Use combined formula

    Total = Top + Bottom - 1 = 10 + 16 - 1 = 25.

  2. Step 2: Cross-check

    From total 25, end rank = 25 - 10 + 1 = 16 ✅

  3. Final Answer:

    25 runners → Option C

  4. Quick Check:

    Top + Bottom - 1 = 25 ✅
Hint: Top + Bottom - 1 = Total.
Common Mistakes: Missing the ‘-1’ correction factor.
5. In a group of players, John ranks 6th from the top and 9th from the bottom. Find total players in the group.
medium
A. 13
B. 15
C. 16
D. 14

Solution

  1. Step 1: Apply formula

    Total = Top + Bottom - 1 = 6 + 9 - 1 = 14.

  2. Step 2: Verify

    14 - 6 + 1 = 9 → matches given bottom rank.

  3. Final Answer:

    14 players → Option D

  4. Quick Check:

    Sum - 1 = 14 ✅
Hint: Add both ranks and subtract 1.
Common Mistakes: Adding both ranks directly without subtracting 1.

Mock Test

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