Proportion Ke Tricky Sawaal | Class 8 Maths Book 1 Ch 7

📘 Class 8 · Ganita Prakash Book 1Ch 7 · Proportional Reasoning-1Post 9 / 9⏱ 25–30 min

Proportion Ke Tricky Sawaal 🧩

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

Trairashika formula (Post 6 — Trairashika: Rule Of Three)?
Ratio mein jodne se kya hota (Post 5 — Ratio Se Tulna: Strong Ya Light?)?
Proportional ki pehchaan (Post 8 — Unit Conversion Aur Ratio)?

Answers dekho

Phala × ichchha ÷ pramana
Ratio badalta
0 → 0, double → double

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 5 — Ratio Se Tulna: Strong Ya Light?, Post 6 — Trairashika: Rule Of Three aur Post 8 — Unit Conversion Aur Ratio dekh lijiye.

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🎬 Kahani: School Quiz Ka Final Round

Quiz master: “Taxi 5 km ka ₹100 leti hai. 10 km ka?” Team A turant: “₹200!” Buzzer: ❌ GALAT. 😲

“Kiraya hai ₹40 fixed + ₹12 per km. 10 km: 40 + 120 = ₹160.”

Team A: “Par trairashika…!” Quiz master: “Trairashika tabhi, jab rishta proportional ho. Final round ka asli sawaal yahi hai.” 🧩

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📖 Concept: Pehla Sawaal Hamesha: “Kya Yeh Proportional Hai?”

💡 Is post ki ek badi baat: Kisi bhi sawaal mein ratio/trairashika lagane se pehle teen test: (1) double karo to double? (2) 0 pe 0? (3) ratio hamesha same? Teeno haan → proportional. Ek bhi na → soch badlo.

Step 1: Trap 1: Fixed hissa (taxi)

5 km: 40 + 60 = ₹100. 10 km: ₹160, ₹200 nahi. Test 2 fail: 0 km pe bhi ₹40.

Tareeka: pehle fixed hatao (100 − 40 = 60), baaki proportional (₹12/km), phir wapas jodo.

Step 2: Trap 2: Umar ka ratio

Aaj Riya 8, Mummy 32 → 1 : 4. 8 saal baad? 16 : 40 = 2 : 5, 1 : 4 nahi!

WHY? Dono mein +8 jod hua, guna nahi (Post 5 — Ratio Se Tulna: Strong Ya Light?: jodne se ratio 1 ki taraf). Umar ka farak (24) hamesha same rehta.

Step 3: Trap 3: Ginti ka round-up (bus)

175 bachche, ek bus mein 40. 175 ÷ 40 = 4.375 → 5 bus (4.375 bus nahi aati!).

WHY? Ratio sahi, par jawab ka matlab dekho: 4 bus mein 15 bachche reh jaate.

Step 4: Trap 4: Ulta rishta (mazdoor)

6 mazdoor 10 din. 12 mazdoor → 5 din, 20 nahi. Test 1 fail: mazdoor double → din aadhe. Yahaan guna (mazdoor × din = 60) same.

Step 5: Sahi proportional: parchhaai

Usi samay 2 m danda, 3 m parchhaai. Ped ki parchhaai 18 m → ped 12 m. Teeno test pass (same samay pe sooraj ka kon same).

🪜 Atak Gaye? Aise Socho

Test 1: double → double?
Test 2: 0 → 0?
Fixed hissa? Pehle hatao.
Ulta? Guna constant.
Jawab ka matlab: round-up chahiye?

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🔐 Deep Concept: Proportional Ki Pehchaan: Ek Line Jo (0, 0) Se Guzre

Graph banao: x-axis pe km, y-axis pe kiraya. Proportional (₹20/km) → line (0, 0) se. Taxi (40 + 12x) → line ₹40 se shuru: seedhi par (0, 0) se nahi.

Umar: Mummy = Riya + 24, line 24 se shuru. Mazdoor-din: line hi nahi, ek curve (guna constant).

Teen tarah ke rishte:

Proportional: y = k × x (ratio same) → trairashika ✅
Fixed + proportional: y = c + k × x (farak ka ratio same) → pehle c hatao
Ulta: x × y = k (guna same) → ulta trairashika

Poore chapter ka central idea: proportional = same factor, same farak nahi (Post 1 — Proportional Badlaav Kya Hai?). Har tricky sawaal mein bas yahi poochho: “factor same hai?” 🎯

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✏️ Solved Examples

Example 1 (Easy): Bijli: ₹100 fixed + ₹6/unit. 150 unit ka bill?

100 + 900 = ₹1000.

Check: 75 unit: ₹550; double unit pe ₹1100 nahi, ₹1000 ✅ (proportional nahi)

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Example 2 (Medium): Bhai : behen umar 3 : 2, 5 saal pehle 5 : 3. Aaj?

3k − 5 : 2k − 5 = 5 : 3 → 9k − 15 = 10k − 25 → k = 10 → 30, 20.

Check: 25 : 15 = 5 : 3 ✅

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Example 3 (NCERT style): Ek din mein 9 mazdoor 36 m deewar. 15 mazdoor?

Per mazdoor 4 m → 60 m (yeh proportional!).

Check: 9 : 36 :: 15 : 60 ✅

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Quiz ka nateeja: Team B ne har sawaal pe pehle “proportional hai?” poochha, aur jeet gayi! 🏆

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🏠 Tricky Proportion Roz Ki Zindagi Mein

🚕 Taxi/auto: minimum kiraya + per km.
💡 Bijli/phone bill: fixed + per unit.
🎂 Umar: farak same, ratio badalta.
🚌 School trip: bus, kursi: round-up.
🌳 Parchhaai: ped ki height bina chadhe.

Thales ne (lagbhag 600 BCE) parchhaai se hi pyramid ki height naapi thi. Proportion ki taakat!

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Double → double	✅ Trairashika	Parchhaai
Fixed shuruaat	✅ Pehle fixed hatao	Taxi
Umar	✅ Farak same	k ke saath
Ek badhe doosra ghate	✅ Guna same	Mazdoor-din
Ginti (bus, kursi)	✅ Round-up	5 bus

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❌→✅ Worked Mistake

Sawaal: Auto ₹30 fixed + ₹15/km. 4 km ka ₹90, to 8 km?

❌ Galat: double → ₹180.

✅ Sahi: 30 + 120 = ₹150. Check: 4 km: 30 + 60 = 90 ✅; 0 km pe ₹30, isliye proportional nahi.

🧠 Rule of thumb: Trairashika se pehle teen test: double → double, 0 → 0, ratio same. Ek fail → soch badlo.

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📝 10 MCQs

Q1. Taxi 40 + 12/km, 10 km?

(a) ₹160

(b) ₹200

(c) ₹120

(d) ₹52

Solution dekho

Sahi jawab: (a)

(a) sahi: Fixed ₹40 + 10 × ₹12 = ₹160 ✅
(b) galat: ₹200 tab hota jab kiraya proportional hota.
(c) galat: ₹120 mein fixed ₹40 bhool gaye.
(d) galat: ₹52 sirf 1 km ka kiraya hai.

Q2. Riya 8, Mummy 32. 8 saal baad?

(a) 2 : 5

(b) 1 : 4

(c) 1 : 2

(d) 3 : 4

Solution dekho

Sahi jawab: (a)

(a) sahi: 8 saal baad 16 : 40 = 2 : 5 ✅
(b) galat: Dono mein +8 jodne se ratio 1 : 4 nahi rehta.
(c) galat: 16 : 40 ko 1 : 2 simplify nahi hota.
(d) galat: 3 : 4 kisi hisaab se nahi aata.

Q3. 175 bachche, 40/bus?

(a) 5

(b) 4

(c) 4.375

(d) 6

Solution dekho

Sahi jawab: (a)

(a) sahi: 4.375 → round-up karke 5 bus ✅
(b) galat: 4 bus mein 15 bachche reh jaate.
(c) galat: Aadhi-adhuri bus nahi aati, round-up karo.
(d) galat: 6 bus zaroorat se ek zyada hai.

Q4. 6 mazdoor 10 din, 12?

(a) 5

(b) 20

(c) 10

(d) 12

Solution dekho

Sahi jawab: (a)

(a) sahi: Mazdoor × din = 60, to 60 ÷ 12 = 5 ✅
(b) galat: Zyada mazdoor se din ghatte, badhte nahi.
(c) galat: Mazdoor badhe to din badalne chahiye.
(d) galat: 12 din ka koi hisaab nahi banta.

Q5. Danda 2 m, parchhaai 3 m; ped parchhaai 18 m?

(a) 12 m

(b) 27 m

(c) 17 m

(d) 6 m

Solution dekho

Sahi jawab: (a)

(a) sahi: Parchhaai × 6, to height 2 × 6 = 12 m ✅
(b) galat: 27 m ulta ratio (3/2) lagaane se aata.
(c) galat: 17 m farak (+1) wali galat soch hai.
(d) galat: 6 m mein factor aadha laga diya.

Q6. Proportional test?

(a) 0 → 0

(b) 0 → 40

(c) Ratio badle

(d) Jod same

Solution dekho

Sahi jawab: (a)

(a) sahi: Proportional rishta 0 pe 0 deta ✅
(b) galat: 0 pe 40 matlab fixed hissa, proportional nahi.
(c) galat: Proportional mein ratio same rehta, badalta nahi.
(d) galat: Same farak proportional ki pehchaan nahi.

Q7. Umar mein kya same?

(a) Farak

(b) Ratio

(c) Guna

(d) Jod

Solution dekho

Sahi jawab: (a)

(a) sahi: Umar ka farak hamesha same rehta ✅
(b) galat: Ratio to har saal badalta hai.
(c) galat: Umar ka guna bhi badalta rehta hai.
(d) galat: Jod har saal 2 se badhta hai.

Q8. Bijli 100 + 6/unit, 150 unit?

(a) ₹1000

(b) ₹900

(c) ₹1100

(d) ₹106

Solution dekho

Sahi jawab: (a)

(a) sahi: ₹100 fixed + 150 × ₹6 = ₹1000 ✅
(b) galat: ₹900 mein fixed ₹100 bhool gaye.
(c) galat: ₹1100 mein fixed do baar jod diya.
(d) galat: ₹106 sirf 1 unit ka bill hai.

Q9. Mazdoor-din kaisa rishta?

(a) Ulta

(b) Seedha

(c) Fixed

(d) Koi nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Ulta: mazdoor × din same rehta ✅
(b) galat: Seedha nahi, mazdoor double to din aadhe.
(c) galat: Fixed hissa wala rishta yeh nahi hai.
(d) galat: Rishta hai: guna constant wala.

Q10. Chapter ka central idea?

(a) Same factor

(b) Same farak

(c) Same jod

(d) Same unit

Solution dekho

Sahi jawab: (a)

(a) sahi: Proportional = same factor (guna) ✅
(b) galat: Same farak proportional ki pehchaan nahi.
(c) galat: Same jod se ratio badal jaata hai.
(d) galat: Unit alag ho sakti, factor same chahiye.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Graph se kaise pata?

Seedhi line (0, 0) se → proportional.

2. Ulta trairashika?

Guna same: 6 × 10 = 12 × x.

3. Kab round-down?

Jab poocho “kitne poore packet bane”: 175 ÷ 40 → 4 poori bus bharegi.

4. Thales kaun?

Greek ganitagya, parchhaai se height.

5. Kya umar sawaal mein k?

Haan, aaj ki umar 3k, 2k.

6. Aage?

Book 2 Ch 3: Proportional Reasoning-2 (Book 2 Ch 3 — Proportional Reasoning-2).

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy Auto 25 + 10/km, 6 km?

Solution dekho

₹85. Check ✅

Q2. Easy Riya 10, papa 40. 10 saal baad ratio?

Solution dekho

20 : 50 = 2 : 5. Check ✅

Q3. Easy 230 log, 50/bus?

Solution dekho

5 bus. Check: 4.6 → 5 ✅

Q4. Easy 8 mazdoor 15 din, 12?

Solution dekho

10 din. Check: 120 ✅

Q5. Medium Danda 1.5 m, parchhaai 2 m; building parchhaai 40 m?

Solution dekho

30 m. Check ✅

Q6. Medium Phone ₹199 + ₹2/GB. ₹239 bill, kitna GB?

Solution dekho

20 GB. Check ✅

Q7. Medium A : B umar 5 : 3, farak 12?

Solution dekho

30, 18. Check ✅

Q8. Medium 4 nal 9 ghante mein tanki. 6 nal?

Solution dekho

6 ghante. Check: 36 ✅

Q9. NCERT style Taxi 3 km ₹96, 7 km ₹176. Fixed aur per km?

Solution dekho

4 km = 80 → ₹20/km, fixed ₹36. Check: 36 + 60 = 96 ✅

Q10. NCERT style Umar 4 : 7, 6 saal baad 5 : 8. Aaj?

Solution dekho

8(4k + 6) = 5(7k + 6) → k = 6 → 24, 42. Check: 30 : 48 = 5 : 8 ✅

Q11. NCERT style Kya 4 : 7 kabhi 1 : 1 banega?

Solution dekho

Nahi, farak 3k hamesha. Check ✅

Q12. NCERT style Kursi: 315 log, 1 row mein 24?

Solution dekho

14 row. Check: 13.125 → 14 ✅

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Kis distance pe taxi (40 + 12/km) aur auto (20 + 16/km) same?

Solution dekho

40 + 12d = 20 + 16d → d = 5. Check: dono ₹100 ✅

Q2. Ratio 2 : 5 umar, kitne saal baad 1 : 2? (aaj 10, 25)

Solution dekho

2(10 + x) = 25 + x → x = 5. Check: 15 : 30 ✅

Q3. 12 mazdoor 8 din mein, 4 din baad 4 chale gaye. Baaki?

Solution dekho

Bacha kaam 48 mazdoor-din ÷ 8 = 6 din. Check ✅

Q4. Parchhaai subah aur dopahar mein same ratio?

Solution dekho

Nahi, sooraj ka kon badalta. Check ✅

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🏆 Olympiad Corner

Q1. Auto 30 + 14/km, ₹170?

Solution dekho

10 km.

Q2. A 3 saal pehle 2 guna B ka; aaj 33, B?

Solution dekho

18.

Q3. 5 machine 12 ghante, 10 ghante ke liye?

Solution dekho

Q4. Ped 9 m, parchhaai 6 m; 15 m pole ki?

Solution dekho

10 m.

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💗 CharuMam Motivation

Ab koi bhi tricky sawaal ho, aapka pehla jawab: “Pehle check karta hoon, proportional hai?” Yahi asli ganit soch hai! 🧩

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🟢 Master Recap

💡 Chaabi: Kisi bhi sawaal mein ratio/trairashika lagane se pehle teen test: (1) double karo to double? (2) 0 pe 0? (3) ratio hamesha same? Teeno haan → proportional. Ek bhi na → soch badlo.
Pehle teen test.
Fixed hissa? Hatao.
Umar: farak same.
Ginti: round-up.
Ulta: guna same.
Same factor, same farak nahi.

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👉 Aage Kya?

Book 2 Ch 3 mein Proportional Reasoning-2: Book 2 Ch 3 — Proportional Reasoning-2.

← Pichla: Post 8 — Unit Conversion Aur Ratio 📚 Chapter 7 ke saare posts Agla chapter: Book 2 Ch 3 — Proportional Reasoning-2 →

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✅ Pehle Yeh Aata Hai?

🎬 Kahani: School Quiz Ka Final Round

📖 Concept: Pehla Sawaal Hamesha: “Kya Yeh Proportional Hai?”

Step 1: Trap 1: Fixed hissa (taxi)

Step 2: Trap 2: Umar ka ratio

Step 3: Trap 3: Ginti ka round-up (bus)

Step 4: Trap 4: Ulta rishta (mazdoor)

Step 5: Sahi proportional: parchhaai

🪜 Atak Gaye? Aise Socho

🔐 Deep Concept: Proportional Ki Pehchaan: Ek Line Jo (0, 0) Se Guzre

✏️ Solved Examples

🏠 Tricky Proportion Roz Ki Zindagi Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

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