Barabar Nahi, Ratio Mein Hissa | Class 8 Maths Book 1 Ch 7

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

Barabar Nahi, Ratio Mein Hissa 🎁

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:

3 : 2 mein kul hisse?
20 ka 3/5?
Hissa : poora (Post 2 — Ratio Kya Hai?)?

Answers dekho

5
12
Fraction of whole

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 2 — Ratio Kya Hai? dekh lijiye.

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🎬 Kahani: Nana Ji Ke Kanche

Nana ji ke paas 20 kanche. Pinku ne 3 ghante bagiche mein madad ki, Chinku ne 2 ghante. 🌳

Nana ji: “Jitni mehnat, utne kanche: 3 : 2 mein baantunga.” Chinku: “10-10 kyun nahi?” Pinku: “To 3 aur 2 kanche, baaki kiske?”

Dono galat! Sahi baantwara: chaliye dekhte hain.

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📖 Concept: Ratio Mein Baantna: Pehle Hisse Gino, Phir Ek Hissa Ka Size

💡 Is post ki ek badi baat: a : b mein baantna = poori cheez ke (a + b) barabar hisse banao; pehle ko a hisse, doosre ko b. Ek hissa = kul ÷ (a + b).

Step 1: Tareeka 1: Hisse (packets)

3 : 2 → kul 5 hisse. 20 ÷ 5 = 4 kanche ek hissa. Pinku 3 × 4 = 12, Chinku 2 × 4 = 8.

WHY? Ratio “har 3 pe 2” kehta: kanche 5-5 ke round mein do (3 Pinku, 2 Chinku). 4 round → 12, 8. Check: 12 + 8 = 20, 12 : 8 = 3 : 2 ✅

Step 2: Tareeka 2: Fraction of whole

Pinku = 3/5 × 20 = 12, Chinku = 2/5 × 20 = 8.

Kab aasaan: jab kul ajeeb ho ya ek hi hissa chahiye.

Step 3: Jab farak diya ho

Ratio 7 : 4, farak 45. Farak = 7 − 4 = 3 hisse = 45 → 1 hissa 15 → 105, 60.

WHY? Hisse ka size hamesha same; farak bhi hisson mein naapo. Check: 105 − 60 = 45 ✅

Step 4: Jab ek hissa diya ho

Ratio 5 : 8, chhota 35 → 1 hissa 7 → bada 56, kul 91.

Step 5: Teen logon mein

₹900 ko 2 : 3 : 4 → 9 hisse, 1 = ₹100 → ₹200, ₹300, ₹400. Check: 900 ✅

🪜 Atak Gaye? Aise Socho

Ratio ke terms jodo = kul hisse.
Jo diya (kul, farak, ek hissa): kitne hisse ke barabar?
Ek hissa nikaalo.
Har ek ka guna karo.
Check: jod (ya farak) aur ratio dono.

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🔐 Deep Concept: Ek Hissa = Ek “Packet”: Har Sawaal Ki Chaabi

Kanche, rupaye, ya mixture: ratio a : b kehta “a packet aur b packet, har packet same size”. Sawaal mein jo bhi diya ho, bas poochho: yeh kitne packet hain?

Kul diya → (a + b) packet
Farak diya → (a − b) packet
Ek ka diya → a ya b packet

Packet size mila, sab mil gaya. Yahi algebra mein “k” hai: a = 3k, b = 2k.

10-10 kyun galat? Barabar baantna = 1 : 1, ratio badal diya. 3 aur 2 kyun galat? Packet size 1 maan liya, jabki 4 hai. Central idea: ratio same factor (packet size) se asli maatra banta. 🎯

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✏️ Solved Examples

Example 1 (Easy): ₹560 ko 3 : 5 mein

8 hisse, 1 = ₹70 → ₹210, ₹350.

Check: 210 + 350 = 560, 210 : 350 = 3 : 5 ✅

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Example 2 (Medium): Do dost ne ₹12000 aur ₹18000 lagaye, munafa ₹7500.

Ratio 2 : 3 → ₹1500 hissa → ₹3000, ₹4500.

Check: 7500 ✅

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Example 3 (NCERT style): 30 litre mix, doodh : paani 7 : 3. Kitna paani jodein ki 3 : 2 ho?

Doodh 21, paani 9. 21 : (9 + x) = 3 : 2 → 9 + x = 14 → x = 5.

Check: 21 : 14 = 3 : 2 ✅ (doodh same raha!)

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Nana ji ka baantwara: 12 aur 8. Chinku khush: “Kam mehnat, kam kanche, insaaf hai!” 🎁

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🏠 Ratio Mein Baantna Roz Ki Zindagi Mein

🤝 Business: paise ke ratio mein munafa.
🧪 Mixture: doodh-paani, cement-ret.
🏡 Zameen/virasat: ratio mein hisse.
🎂 Cake: 2 : 3 mein do group.
💰 Pocket money: umar ke ratio mein.

Mixture mein trick: jo cheez nahi badli (doodh), use fix rakho, phir naya ratio lagao.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Kul diya	✅ (a + b) hisse	20 ÷ 5
Farak diya	✅ (a − b) hisse	45 ÷ 3
Ek hissa diya	✅ Uska term	35 ÷ 5
Sirf ek ka hissa	✅ Fraction	3/5 × kul
Mixture mein jodna	✅ Na badalne wali cheez fix	Doodh same

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❌→✅ Worked Mistake

Sawaal: ₹450 ko 4 : 5 mein.

❌ Galat: 450 ÷ 4 aur 450 ÷ 5, ya ₹4, ₹5 hisse.

✅ Sahi: 9 hisse, 1 = ₹50 → ₹200, ₹250. Check: 450 ✅, 200 : 250 = 4 : 5 ✅

🧠 Rule of thumb: Pehle hisse jodo (a + b), phir kul ÷ hisse. Check: jod aur ratio dono.

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📝 10 MCQs

Q1. 20 ko 3 : 2?

(a) 12, 8

(b) 10, 10

(c) 3, 2

(d) 15, 5

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 5 hisse × 4 ✅
(b) galat: Yeh 1 : 1 hai, isliye yeh galat.
(c) galat: Packet 1 maan liya, isliye yeh galat.
(d) galat: Yeh 3 : 1 hai, isliye yeh galat.

Q2. ₹560 ko 3 : 5?

(a) ₹210, ₹350

(b) ₹70, ₹350

(c) ₹280, ₹280

(d) ₹300, ₹260

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 8 hisse × 70 ✅
(b) galat: ₹70 sirf ek hissa hai, 3 hisse lene the.
(c) galat: Yeh barabar baant diya.
(d) galat: Ratio match nahi, isliye yeh galat.

Q3. 7 : 4, farak 45?

(a) 105, 60

(b) 70, 40

(c) 45, 0

(d) 63, 36

Solution dekho

Sahi jawab: (a)

(a) sahi: Farak = 3 hisse = 45, hissa 15 → 105, 60 ✅
(b) galat: 70 − 40 = 30, farak 45 nahi.
(c) galat: 45 ko ek term bana diya, soch galat.
(d) galat: 63 − 36 = 27, farak 45 nahi.

Q4. 2 : 3 : 4 mein ₹900?

(a) 200, 300, 400

(b) 300, 300, 300

(c) 180, 270, 450

(d) 100, 200, 600

Solution dekho

Sahi jawab: (a)

(a) sahi: Bilkul sahi jawab: 9 hisse ✅
(b) galat: Barabar baanta, isliye yeh galat.
(c) galat: Jod 900, par ratio galat.
(d) galat: Ratio galat, isliye yeh option sahi nahi.

Q5. 5 : 8, chhota 35, bada?

(a) 56

(b) 38

(c) 40

(d) 91

Solution dekho

Sahi jawab: (a)

(a) sahi: 35 ÷ 5 = 7, bada 8 × 7 = 56 ✅
(b) galat: 38 mein farak 3 jod diya.
(c) galat: 40 mein packet size galat liya.
(d) galat: 91 to kul hai, bada nahi.

Q6. Kul hisse 4 : 5?

(a) 9

(b) 20

(c) 1

(d) 4

Solution dekho

Sahi jawab: (a)

(a) sahi: Bilkul sahi jawab: 4 + 5 ✅
(b) galat: Guna nahi, isliye yeh galat.
(c) galat: Farak nahi, isliye yeh galat.
(d) galat: Sirf ek term, isliye yeh galat.

Q7. Mixture mein paani jodne pe kya same?

(a) Doodh

(b) Paani

(c) Ratio

(d) Kul

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: Doodh fix ✅
(b) galat: Paani badla, isliye yeh galat.
(c) galat: Ratio badla, isliye yeh galat.
(d) galat: Kul badla, isliye yeh galat.

Q8. Munafa ₹12000 : ₹18000, ₹7500?

(a) 3000, 4500

(b) 3750, 3750

(c) 2500, 5000

(d) 4500, 3000

Solution dekho

Sahi jawab: (a)

(a) sahi: Bilkul sahi jawab: 2 : 3 ✅
(b) galat: Barabar nahi, isliye yeh galat.
(c) galat: 1 : 2 galat, isliye yeh option sahi nahi.
(d) galat: Order ulta, isliye yeh galat.

Q9. Packet ka algebra naam?

(a) k

(b) x²

(c) π

(d) 0

Solution dekho

Sahi jawab: (a)

(a) sahi: 3k, 2k: k ek packet ka size ✅
(b) galat: x² square hai, packet nahi.
(c) galat: π circle ka number hai, packet nahi.
(d) galat: 0 packet ho to kuch baantna hi nahi.

Q10. ₹450 ko 4 : 5?

(a) 200, 250

(b) 112.5, 90

(c) 4, 5

(d) 225, 225

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 9 hisse × 50 ✅
(b) galat: Alag bhaag galat, isliye yeh option sahi nahi.
(c) galat: Packet 1 maan liya, isliye yeh galat.
(d) galat: Barabar baanta, isliye yeh galat.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Agar baantna whole na aaye?

Kanche jaise mein ratio check karo; rupaye mein paise chalte.

2. Ratio aur fraction mein hisse?

a : b mein pehla = a/(a + b) of kul.

3. Teen se zyada log?

Same tareeka: sab terms jodo.

4. Farak aur kul dono?

Koi bhi ek kaafi hai.

5. Munafa ratio kaise?

Lagaye paise (aur samay) ke ratio mein.

6. Aage?

Alag unit ke ratio: Post 8 — Unit Conversion Aur Ratio.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy 35 ko 4 : 3?

Solution dekho

20, 15. Check ✅

Q2. Easy ₹720 ko 5 : 7?

Solution dekho

₹300, ₹420. Check ✅

Q3. Easy 48 ko 1 : 3?

Solution dekho

12, 36. Check ✅

Q4. Easy ₹1000 ko 3 : 2 : 5?

Solution dekho

300, 200, 500. Check ✅

Q5. Medium Ratio 9 : 5, farak 28?

Solution dekho

1 hissa 7 → 63, 35. Check ✅

Q6. Medium Ratio 2 : 7, bada 63. Kul?

Solution dekho

1 hissa 9 → 81. Check ✅

Q7. Medium Cement : ret 1 : 5, kul 54 bori?

Solution dekho

9, 45. Check ✅

Q8. Medium Umar ratio 4 : 5, jod 63?

Solution dekho

28, 35. Check ✅

Q9. NCERT style 40 l mix, doodh : paani 3 : 1. Kitna paani ki 2 : 1?

Solution dekho

Doodh 30, paani 10 → 15 → 5 l. Check ✅

Q10. NCERT style ₹24000, ₹36000, ₹40000 lagaye, munafa ₹15000?

Solution dekho

6 : 9 : 10 → 3600, 5400, 6000. Check ✅

Q11. NCERT style A : B = 3 : 4, B : C = 6 : 5, kul 155?

Solution dekho

9 : 12 : 10 → 31 hisse, 1 = 5 → 45, 60, 50. Check: 155 ✅, 45 : 60 = 3 : 4, 60 : 50 = 6 : 5 ✅

Q12. NCERT style Kanche 5 : 3 mein, A ne B ko 4 diye, ab barabar. Kul?

Solution dekho

2 hisse = 8 → hissa 4 → 32. Check: 20 − 4 = 12 + 4 ✅

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Ratio 3 : 5, dono mein 10 jodne pe 5 : 7. Numbers?

Solution dekho

7(3k + 10) = 5(5k + 10) → k = 5 → 15, 25. Check: 25 : 35 ✅

Q2. Gold : copper 7 : 2 aur 7 : 11 ke barabar vajan mila diye?

Solution dekho

LCM 18: 14 : 4 + 7 : 11 → 21 : 15 = 7 : 5. Check ✅

Q3. Kya 25 kanche 3 : 2 mein?

Solution dekho

Haan: 15, 10. Check ✅

Q4. Kya 24 kanche 3 : 2 mein?

Solution dekho

Nahi (24/5 whole nahi). Check ✅

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🏆 Olympiad Corner

Q1. 84 ko 5 : 7?

Solution dekho

35, 49.

Q2. Ratio 11 : 7, farak 20?

Solution dekho

55, 35.

Q3. ₹1350 ko 1/2 : 1/3?

Solution dekho

3 : 2 → 810, 540.

Q4. a : b = 2 : 3, a = 18. a + b?

Solution dekho

45.

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💗 CharuMam Motivation

Ab baantwara karte waqt koi jhagda nahi: packet gino, size nikaalo, insaaf ho gaya! 🎁

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🟢 Master Recap

💡 Chaabi: a : b mein baantna = poori cheez ke (a + b) barabar hisse banao; pehle ko a hisse, doosre ko b. Ek hissa = kul ÷ (a + b).
Kul hisse = a + b.
Ek hissa = kul ÷ hisse.
Farak = (a − b) hisse.
Fraction: a/(a + b) × kul.
Mixture: na badalne wali fix.
Check jod aur ratio.

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👉 Aage Kya?

1200 sq ft vs 110 sq m? Post 8 — Unit Conversion Aur Ratio.

← Pichla: Post 6 — Trairashika: Rule Of Three 📚 Chapter 7 ke saare posts Agla: Post 8 — Unit Conversion Aur Ratio →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Nana Ji Ke Kanche

📖 Concept: Ratio Mein Baantna: Pehle Hisse Gino, Phir Ek Hissa Ka Size

Step 1: Tareeka 1: Hisse (packets)

Step 2: Tareeka 2: Fraction of whole

Step 3: Jab farak diya ho

Step 4: Jab ek hissa diya ho

Step 5: Teen logon mein

🪜 Atak Gaye? Aise Socho

🔐 Deep Concept: Ek Hissa = Ek “Packet”: Har Sawaal Ki Chaabi

✏️ Solved Examples

🏠 Ratio Mein Baantna 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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