Ratio Se Tulna: Strong Ya Light? | Class 8 Maths Book 1 Ch 7

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📘 Class 8 · Ganita Prakash Book 1Ch 7 · Proportional Reasoning-1Post 5 / 9⏱ 25–30 min
Ratio Se Tulna: Strong Ya Light? ☕
IS POST MEIN
Pehle Yeh Aata Hai?KahaniConceptDeep ConceptExamplesReal LifeGalti10 MCQsFAQsPracticeHOTSOlympiadRecap

✅ Pehle Yeh Aata Hai?

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

  1. 2/5 decimal mein?
  2. 3/7 lagbhag?
  3. Cross product test (Post 4 — Proportion Kya Hai? (:: Ka Matlab))?
Answers dekho
  1. 0.4
  2. 0.43
  3. a × d vs b × c

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 4 — Proportion Kya Hai? (:: Ka Matlab) dekh lijiye.

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🎬 Kahani: Tapri Pe Chai Ki Behes

Chowk ki do tapri. Raju bhaiya: 2 cup kadha (patti wala paani) : 5 cup doodh. Shyam bhaiya: 3 cup kadha : 7 cup doodh. ☕

Papa ko kadak chai pasand. “Shyam ke yahan kadha zyada (3), wahi strong!” Mummy: “Par doodh bhi zyada (7)…”

Ratio barabar nahi, to kaunsa strong? Chaliye teen tareeke se pakka karte hain.

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📖 Concept: Tulna Ka Raaz: Ek Term Barabar Karo, Phir Dekho

💡 Is post ki ek badi baat: Do ratio tab tak seedhe compare nahi ho sakte jab tak ek term (ya poora) same base pe na ho. Base barabar karo (common term, per-unit, ya decimal), phir doosra term batata kaun zyada.

Step 1: Tareeka 1: Doodh barabar karo (LCM)

2 : 5 → × 7 → 14 : 35. 3 : 7 → × 5 → 15 : 35. Ab dono mein 35 cup doodh; kadha 14 vs 15 → Shyam strong ✅.

WHY? Same factor se guna = same swaad (Post 4 — Proportion Kya Hai? (:: Ka Matlab)). Doodh barabar karke sirf kadha ka farak dikhta. Kab aasaan: chhote second terms.

Step 2: Tareeka 2: Per cup doodh (decimal)

Raju: 2/5 = 0.40 kadha har cup doodh pe. Shyam: 3/7 ≈ 0.43. Shyam zyada ✅.

Kab aasaan: kai options, calculator ho, ya percent mein sochna ho.

Step 3: Tareeka 3: Cross product

2 × 7 = 14, 5 × 3 = 15. 14 < 15 → 2/5 < 3/7 ✅.

WHY? Yeh tareeka 1 ka chhota roop hai! 14 aur 15 wahi kadha ke cup hain jo 35 doodh pe aaye.

Step 4: Hissa : poora se bhi

Raju: kadha/kul = 2/7 ≈ 0.286. Shyam: 3/10 = 0.30 → Shyam strong. Same jawab!

WHY? Jo ratio kadha : doodh mein bada, woh kadha : kul mein bhi bada. Bas dono taraf ek hi tarah ka ratio lo.

Step 5: Per-unit daam

Biscuit: 4 packet ₹70 ya 6 packet ₹100? 70/4 = ₹17.50, 100/6 ≈ ₹16.67 → 6 wala sasta.

Check (LCM 12): 12 packet: ₹210 vs ₹200 ✅

🪜 Atak Gaye? Aise Socho

  • Dono ratio same order mein likho (kadha : doodh).
  • Doosra term barabar karo (LCM) ya decimal nikalo.
  • Pehla term compare karo.
  • Cross product se pakka karo.
  • Jawab ko kahaani mein bolo: “Shyam ki chai kadak”.

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🔐 Deep Concept: Jodne Se Ratio Kyun Badalta: “Same Farak” Ka Dhokha

Raju ne socha: “2 : 5 mein 1 cup kadha aur 1 cup doodh dono jod do, 3 : 6 ban jayega, swaad same.” Par 3 : 6 = 1 : 2 = 0.5, jabki 2 : 5 = 0.4. Chai kadak ho gayi!

WHY? +1 kadha, 2 pe 50% badhaav. +1 doodh, 5 pe sirf 20%. Badhaav ka factor alag, isliye rishta badla.

General sach: agar a/b < 1 aur dono mein same number jodo, ratio 1 ki taraf khiskta hai (2 : 5 → 3 : 6 → 4 : 7 → … → lagbhag 1 : 1).

Unifying idea: ratio sirf guna se bachta, jod se nahi. Tulna ke liye bhi guna (common base) chahiye. Central idea fir wahi: same factor, same farak nahi. 🎯

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✏️ Solved Examples

Example 1 (Easy): Kaun zyada meetha: 3 chammach 4 glass, ya 5 chammach 7 glass?

Cross: 3 × 7 = 21, 4 × 5 = 20 → 3 : 4 zyada.

Check: 0.75 vs 0.714 ✅

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Example 2 (Medium): Class A: 12 paas 15 mein, class B: 17 paas 20 mein. Behtar?

A 80%, B 85% → B.

Check: cross 12 × 20 = 240 < 15 × 17 = 255 ✅

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Example 3 (NCERT style): 500 ml ₹45 ya 750 ml ₹66?

Per 100 ml: ₹9 vs ₹8.80 → 750 ml sasta.

Check: 1500 ml: ₹135 vs ₹132 ✅

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Papa ka faisla: Shyam bhaiya ki chai (3 : 7), kyunki har 35 cup doodh pe 15 cup kadha vs 14. Farak chhota, par kadak-pasand zabaan pakad leti! ☕

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🏠 Tulna Roz Ki Zindagi Mein

  • 🛒 Shopping: bada pack hamesha sasta? Per-unit nikaalo.
  • 🏏 Cricket: 45 run 30 ball vs 60 run 45 ball: strike rate.
  • 📚 Result: alag total marks: percent mein tulna.
  • 🌱 Khad: do mix mein kaunsa gaadha.
  • 🚗 Mileage: 300 km 20 litre vs 420 km 30 litre.

Mileage: 15 km/l vs 14 km/l → pehli gaadi behtar. Bina ratio ke “420 zyada hai” jaisi galti ho jaati!

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🧭 Kab Use Karein, Kab Nahi

SituationKya kareinKyun
Chhote second terms✅ LCM se barabar14 : 35 vs 15 : 35
Kai options✅ Decimal/per-unit0.40, 0.43
Sirf do ratio, jaldi✅ Cross product14 vs 15
Daam ki tulna✅ Per unit₹/100 ml
Percent chahiye✅ Hissa : poora80% vs 85%

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❌→✅ Worked Mistake

Sawaal: 4 : 9 aur 5 : 11 mein bada?

❌ Galat: “5 > 4, to 5 : 11 bada” ya “farak 5 vs 6”.

✅ Sahi: cross: 4 × 11 = 44, 9 × 5 = 45 → 5 : 11 bada (yahaan sahi, par tukke se nahi!). Check: 0.444 vs 0.4545 ✅

Ab 3 : 4 vs 4 : 6 dekho: “4 > 3” kehta doosra bada, par 0.75 > 0.67 → pehla bada. Pehle term ki tulna dhokha deti.

🧠 Rule of thumb: Ek term dekh ke ratio compare mat karo. Base barabar karo (LCM/decimal/cross), phir bolo.

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📝 10 MCQs

Q1. 2 : 5 vs 3 : 7 kadak?

(a) 3 : 7
(b) 2 : 5
(c) Same
(d) Pata nahi
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 15/35 > 14/35 ✅
  • (b) galat: 0.40 < 0.43 hai, isliye yeh galat.
  • (c) galat: Cross 14 ≠ 15, isliye yeh galat.
  • (d) galat: Teen tareeke se pata, isliye yeh galat.

Q2. 3 : 4 vs 4 : 6 bada?

(a) 3 : 4
(b) 4 : 6
(c) Same
(d) Dono chhote
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 0.75 > 0.67 ✅
  • (b) galat: Pehle term ka dhokha, isliye yeh galat.
  • (c) galat: Cross 18 ≠ 16, isliye yeh galat.
  • (d) galat: Tulna ho sakti hai, isliye yeh galat.

Q3. 4 packet ₹70 ya 6 ₹100: sasta?

(a) 6 wala
(b) 4 wala
(c) Same
(d) Bada hamesha mehnga
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: ₹16.67 < ₹17.50 ✅
  • (b) galat: Per packet zyada hai, isliye yeh galat.
  • (c) galat: Per packet alag hai, isliye yeh galat.
  • (d) galat: Yahaan bada sasta nikla.

Q4. 2 : 5 dono mein +1 = ?

(a) 3 : 6 (alag)
(b) Same ratio
(c) 2 : 5
(d) 1 : 1
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 0.5 ≠ 0.4 ✅
  • (b) galat: Jod se ratio badalta, isliye yeh galat.
  • (c) galat: Badal gaya hai, isliye yeh galat.
  • (d) galat: Bahut jod ke paas aata.

Q5. Cross 4 : 9 vs 5 : 11?

(a) 44 vs 45
(b) 36 vs 55
(c) 20 vs 99
(d) Galat tareeka
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 4 × 11, 9 × 5 ✅
  • (b) galat: Galat jodi ka guna, isliye yeh option sahi nahi.
  • (c) galat: Galat jodi ka guna, isliye yeh option sahi nahi.
  • (d) galat: Sahi tareeka hai, isliye yeh galat.

Q6. 12/15 vs 17/20 behtar?

(a) 17/20
(b) 12/15
(c) Same
(d) Kam marks wala
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 85% > 80% ✅
  • (b) galat: 80% kam hai, isliye yeh galat.
  • (c) galat: Percent alag hain, isliye yeh galat.
  • (d) galat: Percent dekho, isliye yeh galat.

Q7. Kadha : kul mein bhi tulna?

(a) Haan, same jawab
(b) Nahi
(c) Ulta jawab
(d) Sirf decimal
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 2/7 < 3/10 ✅
  • (b) galat: Chal jaata hai, isliye yeh galat.
  • (c) galat: Same aata hai, isliye yeh galat.
  • (d) galat: Kisi bhi tareeke se, isliye yeh galat.

Q8. 300 km 20 l vs 420 km 30 l?

(a) Pehli behtar
(b) Doosri behtar
(c) Same
(d) 420 zyada to doosri
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 15 > 14 km/l ✅
  • (b) galat: 14 km/l kam hai, isliye yeh galat.
  • (c) galat: Alag mileage, isliye yeh galat.
  • (d) galat: Kul doori se nahi, isliye yeh galat.

Q9. Tulna ka raaz?

(a) Base barabar karo
(b) Bada number dekho
(c) Farak dekho
(d) Jod dekho
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: Common term/unit ✅
  • (b) galat: Ek number dhokha deta.
  • (c) galat: Farak se ratio nahi, isliye yeh galat.
  • (d) galat: Jod se nahi, isliye yeh galat.

Q10. 500 ml ₹45, 750 ml ₹66 per 100 ml?

(a) ₹9, ₹8.80
(b) ₹9, ₹9
(c) ₹8, ₹9
(d) ₹45, ₹66
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: Sahi bhaag ✅
  • (b) galat: 66/7.5 = 8.80, isliye yeh galat.
  • (c) galat: 45/5 = 9, isliye yeh galat.
  • (d) galat: Per 100 ml chahiye, isliye yeh galat.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. LCM ya cross?

Cross jaldi; LCM se kahaani samajh aati.

2. Teen ratio?

Sabke decimal nikaalo ya sabka common term.

3. Bada pack hamesha sasta?

Nahi! Per-unit nikaal ke dekho.

4. Percent aur ratio?

Percent = hissa : poora with poora 100 (Percentage Kya Hai?).

5. Kya same farak = same ratio?

Nahi, Post 1 — Proportional Badlaav Kya Hai? ka central idea.

6. Aage?

Ek se zyada maatra kaise nikaalein: Post 6 — Trairashika: Rule Of Three.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy 3 : 5 vs 4 : 7 bada?

Solution dekho

3 : 5. Check: 21 > 20 ✅

Q2. Easy 5 : 8 vs 7 : 12?

Solution dekho

5 : 8. Check: 60 > 56 ✅

Q3. Easy 1 kg ₹60 ya 2.5 kg ₹140?

Solution dekho

₹60 vs ₹56 → 2.5 kg sasta. Check ✅

Q4. Easy 2 : 3 vs 6 : 9?

Solution dekho

Same. Check: 18 = 18 ✅

Q5. Medium A: 18/25, B: 22/30 behtar?

Solution dekho

72% vs 73.3% → B. Check: 540 < 550 ✅

Q6. Medium 45 run 30 ball vs 60 run 45 ball?

Solution dekho

150 vs 133.3 → pehla. Check: 45 × 45 = 2025 > 30 × 60 = 1800 ✅

Q7. Medium 4 : 7 dono mein 3 jodo: ratio badha ya ghata?

Solution dekho

7 : 10 = 0.7 > 0.571 → badha. Check ✅

Q8. Medium Teen ratio 2 : 3, 5 : 8, 3 : 5: sabse bada?

Solution dekho

0.667, 0.625, 0.6 → 2 : 3. Check ✅

Q9. NCERT style 6 : 5 dono mein 2 jodo: badha ya ghata?

Solution dekho

8 : 7 ≈ 1.14 < 1.2 → ghata (1 ki taraf). Check ✅

Q10. NCERT style x : 9 > 5 : 6, sabse chhota whole x?

Solution dekho

6x > 45 → x = 8. Check: 48 > 45 ✅

Q11. NCERT style 200 g ₹48, 350 g ₹80, 500 g ₹118: sasta?

Solution dekho

Per 100 g: 24, 22.86, 23.6 → 350 g. Check ✅

Q12. NCERT style a : b = 3 : 4. a : b ya (a + 1) : (b + 1) bada?

Solution dekho

Doosra (1 ki taraf). Check: k = 1: 4 : 5 = 0.8 > 0.75 ✅

Answer Key — charumam.com exclusive

🧠 HOTS (Sochne Wale Sawaal)

Q1. a/b < c/d to (a + c)/(b + d) kahaan?

Solution dekho

Beech mein. Check: 2/5 < 3/7 → 5/12 ≈ 0.417 beech ✅

Q2. Do mix mila diye (2 : 5 aur 3 : 7, ek-ek jug): naya?

Solution dekho

5 : 12. Check: 0.4 < 0.417 < 0.43 ✅

Q3. Ratio 1 : 1 mein dono mein 5 jodo?

Solution dekho

Same 1 : 1. Check ✅

Q4. Kaun bada: 11/12 ya 12/13?

Solution dekho

143 < 144 → 12/13. Check ✅

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🏆 Olympiad Corner

Q1. 5/9 vs 6/11?

Solution dekho

5/9 (55 > 54).

Q2. Sabse chhota: 3/7, 4/9, 5/11?

Solution dekho

3/7.

Q3. 7 : 10 dono mein se 3 ghatao?

Solution dekho

4 : 7, chhota.

Q4. ₹84 mein 12 ya ₹120 mein 16: sasta?

Solution dekho

₹7 vs ₹7.50 → pehla.

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Ab tapri ho ya supermarket, aap dhokha nahi khaoge. Base barabar, phir tulna! ☕

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🟢 Master Recap

  • 💡 Chaabi: Do ratio tab tak seedhe compare nahi ho sakte jab tak ek term (ya poora) same base pe na ho. Base barabar karo (common term, per-unit, ya decimal), phir doosra term batata kaun zyada.
  • Base barabar karo, phir tulna.
  • LCM, decimal, cross: teen tareeke.
  • Per-unit daam.
  • Jodne se ratio badalta (1 ki taraf).
  • Ek term dekh ke mat bolo.
  • Same factor, same farak nahi.

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👉 Aage Kya?

50 logon ke liye 8 kg, to 175 ke liye? Post 6 — Trairashika: Rule Of Three.

← Pichla: Post 4 — Proportion Kya Hai? (:: Ka Matlab)📚 Chapter 7 ke saare postsAgla: Post 6 — Trairashika: Rule Of Three →

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