Ch 8: Ranking, Order & Sequence | Reasoning

Dosto, is chapter mein bachche line mein khade hote hain ya class mein rank aati hai — aur poocha jata hai "kul kitne hain?", "doosre sire se kaunse number par hai?", "do ke beech kitne log hain?"

Sabse achhi baat — poore chapter mein bas ek formula hai: Total = Left + Right − 1. Aur usi ka ulta roop baaki sawal solve kar deta hai.

CET Group D mein isse 1–2 questions aate hain, aur ye sabse pakke marks hain — bas −1 lagana mat bhoolna! Chalo shuru karein. 💪

1. ⭐ MASTER FORMULA — Total = Left + Right − 1

−1 kyun? Kyunki jis bande ki baat ho rahi hai, wo dono ginti mein aa jata hai — ek baar hata do.

⭐ Formula aur uske teen roop Total = Left + Right − 1
Left = Total − Right + 1 · Right = Total − Left + 1
Class ki rank mein: Total = Top se rank + Bottom se rank − 1 (left/right ki jagah top/bottom).

✏️ Solved Example 1 — dono taraf ki position di ho Ek ladka line mein left se 7th aur right se 9th hai. Kul kitne bachche?
→ 7 + 9 − 1 = 15 ✓

✏️ Solved Example 2 — doosre sire se position 40 bachchon ki line mein A left se 12th hai. Right se kaunse number par?
→ 40 − 12 + 1 = 29 ✓

✏️ Solved Example 3 — class rank 45 bachchon ki class mein Ravi top se 15th hai. Neeche se?
→ 45 − 15 + 1 = 31 ✓

2. "Beech mein kitne log?" ⭐

⭐ Dono ki position EK HI TARAF se nikalo, phir antar − 1 Solved Example: 30 bachchon ki line mein A left se 10th aur B right se 12th hai. Beech mein kitne?
Step 1: B ki left wali position = 30 − 12 + 1 = 19
Step 2: Beech ke log = 19 − 10 − 1 = 8 ✓
⚠️ Jab tak dono positions ek hi sire se na hon, ghatana mat!

3. Interchange (jagah badalna) wale sawal

⭐ Jagah badalne par har banda doosre ki position le leta hai Solved Example: Kamal left se 9th aur Vimal right se 8th hai. Jagah badalne par Kamal left se 17th ho jata hai. Kul bachche?
Step 1: Kamal ab Vimal ki jagah par hai → Vimal ki left wali position = 17
Step 2: Vimal right se 8th bhi tha → Total = 17 + 8 − 1 = 24 ✓

4. "Kitne peeche/aage hain?" (position se ginti)

✏️ Solved Example 20 logon ki queue mein Sita aage se 6th hai. Uske peeche kitne log?
→ 20 − 6 = 14 ✓ (yahan −1 nahi lagta, kyunki Sita khud ginti se bahar hai)
Farq samjho: "position" poochne par +1 wala formula, "kitne log peeche/aage" poochne par seedha ghatana.

5. Height / Age wali Ordering

⭐ Sab shartein ek line mein likho: sabse bada > … > sabse chhota Solved Example: A, B se lamba par C se chhota. D sabse lamba. Doosra sabse lamba kaun?
Step 1: C > A > B
Step 2: D sabse lamba → D > C > A > B
Step 3: Doosra sabse lamba = C ✓

📌 Ordering ka tarika Har shart ko > ke nishan se likho aur dhire-dhire ek lambi line banao. Naam yaad rakhne ki koshish mat karo — kagaz par line hi kaafi hai.

✏️ Type 1 — "Kul kitne hain?" Dono taraf ki position di hogi → L + R − 1. 18th left + 22nd right → 39.

✏️ Type 2 — "Doosre sire se kaunsa number?" Total diya hoga → Total − position + 1. Row of 50 mein 27th left → right se 24th.

✏️ Type 3 — "Beech mein kitne log?" Pehle dono ko ek hi sire ki position mein badlo, phir antar − 1.

✏️ Type 4 — Interchange Badalne ke baad jo nayi position mili hai, wo doosre bande ki purani position hai — wahi se total nikal jata hai.

✏️ Type 5 — Height/age ordering Shartein > mein likho, ek line banao, phir "teesra sabse lamba/chhota" gino. Line ke dono sire par dhyan do.

Trick 1: Ek formula sab par
Total = L + R − 1
Isi ko ghuma ke: L = T − R + 1, R = T − L + 1. Teen alag formule ratne ki zaroorat nahi — ek hi kaafi hai.

Trick 2: −1 ka matlab samjho
Wo banda do baar gina gaya
Ratne se behtar hai samajhna — jab bhi khud wo banda dono ginti mein aaye, ek baar hatana padta hai.

Trick 3: "Beech mein" wale mein ek sira fix karo
Dono ko LEFT wali position banao
Ek left se, doosra right se — aise seedha ghatane par answer galat aayega. Pehle dono ko ek hi bhasha mein lao.

Trick 4: "Position" vs "kitne log" ka farq
Position → +1 · Kitne log → seedha ghatao
"6th from front" wale ke peeche 20−6 = 14 log. Par uski position peeche se 20−6+1 = 15th hogi. Ek shabd, do alag answer!

Trick 5: Chhota diagram banao
◻◻◻ X ◻◻◻ — bas itna
Confusion ho to 8-10 dabbe bana ke position rakh do. 10 second ka diagram galti bacha leta hai.

❌ Galti 1: −1 bhool jana 7th left + 9th right = 15, 16 nahi. Ye chapter ki sabse badi aur sabse common galti hai — option mein 16 zaroor hoga!

❌ Galti 2: "Beech mein" wale mein alag-alag sire A left se 10th, B right se 12th → seedha 12−10 mat karo. Pehle B ko left wali position (19) banao, phir 19−10−1 = 8.

❌ Galti 3: "Kitne log peeche" mein +1 laga dena 20 mein 6th wale ke peeche 14 log hain (20−6). Yahan +1 nahi lagta — wo khud ginti mein nahi aata.

❌ Galti 4: Rank aur position mila dena "Top se 15th" ka matlab class mein 14 log usse aage hain. Rank ke sawal mein bhi wahi formula chalta hai — bas left/right ki jagah top/bottom.

❌ Galti 5: Ordering mein "chhota/bada" ulta karna "A, B se lamba par C se chhota" → C > A > B. Jaldi mein log A ko sabse lamba likh dete hain. Har shart ko alag likh kar jodo.

Master formula?tap 👆

Total = Left + Right − 1

−1 kyun lagta hai?tap 👆

Wo banda do baar gina jata hai

Total aur left se position pata → right?tap 👆

Total − Left + 1

7th left + 9th right → total?tap 👆

15

Row of 40, 12th left → right se?tap 👆

29 (40 − 12 + 1)

Class 45, top se 15th → neeche se?tap 👆

31

"Beech mein kitne" ka tarika?tap 👆

Dono ko ek sire ki position banao → antar − 1

Queue 20, 6th from front → peeche kitne?tap 👆

14 (yahan +1 NAHI)

"Position" vs "kitne log"?tap 👆

Position → +1 · kitne log → seedha ghatao

Interchange ke baad nayi position?tap 👆

= doosre bande ki purani position

9th left + 8th right, badalne par 17th left → total?tap 👆

24 (17 + 8 − 1)

9th top + 12th bottom → total?tap 👆

20

Ordering kaise likhein?tap 👆

Ek line mein > ke nishan se

"A, B se lamba par C se chhota" = ?tap 👆

C > A > B

14th front + 16th back → total?tap 👆

29

Row 50, A 22nd left, B usse 5 aage → B right se?tap 👆

24 (B = 27 left)

Rank wale sawal mein formula?tap 👆

Wahi — top + bottom − 1

Confusion ho to?tap 👆

Chhote dabbe (◻◻◻) bana lo

Sawal	Formula
Kul kitne (dono position se)	L + R − 1
Right se position	Total − Left + 1
Left se position	Total − Right + 1
Class rank (kul)	Top + Bottom − 1
Beech ke log	Ek sire ki position → antar − 1
Kitne peeche hain	Total − position (+1 nahi)
Interchange	Nayi position = doosre ki purani
7L + 9R	Total 15
Row 40, 12th L	Right se 29
Class 45, 15th top	Bottom se 31
Ordering	Ek line: bada > chhota
Sabse badi galti	−1 bhoolna

🎯 Score: 0 / 0 Total questions: 14

Practice (exam-style)

Q1. In a row of 40 students, A is 12th from the left. What is his position from the right?

💡 40 − 12 + 1 = 29.

Practice (exam-style)

Q2. In a row, B is 7th from the left and 9th from the right. How many persons are there in the row?

💡 7 + 9 − 1 = 15 (−1 bhoolne par 16 aa jata hai — wahi trap hai).

Practice (exam-style)

Q3. In a class of 45 students, Ravi's rank is 15th from the top. What is his rank from the bottom?

💡 45 − 15 + 1 = 31.

Practice (exam-style)

Q4. In a row of 30 students, A is 10th from the left and B is 12th from the right. How many students are there between them?

💡 B left se = 30−12+1 = 19 → beech = 19 − 10 − 1 = 8.

Practice (exam-style)

Q5. In a row of 25 boys, Ravi is 11th from the left and Amit is 9th from the right. How many boys are between them?

💡 Amit left se = 25−9+1 = 17 → beech = 17 − 11 − 1 = 5.

Practice (exam-style)

Q6. Rahul is 18th from the left and 22nd from the right in a row. How many persons are in the row?

💡 18 + 22 − 1 = 39.

Practice (exam-style)

Q7. In a queue of 20 people, Sita is 6th from the front. How many people are behind her?

💡 20 − 6 = 14 (yahan +1 nahi lagta — Sita khud ginti mein nahi).

Practice (exam-style)

Q8. In a row of 50 children, A is 22nd from the left. B is 5 places to the right of A. What is B's position from the right?

💡 B left se = 22 + 5 = 27 → right se = 50 − 27 + 1 = 24.

Practice (exam-style)

Q9. A boy is 9th from the top and 12th from the bottom in a class. How many students are there in the class?

💡 9 + 12 − 1 = 20.

Practice (exam-style)

Q10. Kamal is 9th from the left and Vimal is 8th from the right in a row. If they interchange their positions, Kamal becomes 17th from the left. How many children are in the row?

💡 Kamal ab Vimal ki jagah par → Vimal left se 17th tha; total = 17 + 8 − 1 = 24.

Practice (exam-style)

Q11. A is taller than B but shorter than C. D is the tallest of all. Who is the second tallest?

💡 C > A > B aur D sabse lamba → D > C > A > B → doosra = C.

Practice (exam-style)

Q12. In a row of 35 students, one student is 10th from the left and another is 15th from the right. How many students are between them?

💡 Doosra left se = 35−15+1 = 21 → beech = 21 − 10 − 1 = 10.

Practice (exam-style)

Q13. Mohan is 14th from the front and 16th from the back in a queue. How many people are in the queue?

💡 14 + 16 − 1 = 29.

Practice (exam-style)

Q14. Among five friends, P is taller than Q, R is taller than P, S is shorter than Q and T is the tallest. Who is the shortest?

💡 T > R > P > Q > S → sabse chhota = S.

Poora chapter ek formula par khada hai — Total = Left + Right − 1 (aur usi ko ghuma ke: Left = Total − Right + 1). −1 kyun? Kyunki jis bande ki baat ho rahi hai wo dono ginti mein aa jata hai. Class rank mein bhi wahi formula, bas left/right ki jagah top/bottom. "Beech mein kitne log" poocha jaye to pehle dono ko ek hi sire ki position mein badlo, phir antar − 1. Aur ek zaroori farq: "position" poochne par +1 lagta hai, par "kitne log peeche hain" poochne par seedha ghatana hai (20 mein 6th ke peeche 14). Interchange wale sawal mein nayi position = doosre bande ki purani position. 🚀