Percentage Ki Galtiyan Pakdo | Class 8 Maths Book 2 Ch 1 (Fractions in Disguise)

📘 Class 8 · Ganita Prakash Book 2Ch 1 · Fractions in DisguisePost 14 / 14⏱ 25–30 min

Percentage Ki Galtiyan Pakdo 🕵️

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:

1.5 × 0.5 = ?
₹500 pe ₹250 profit: CP pe kitna %?
0.99 × 100 = ?

Answers dekho

0.75
50%
99

Teeno sahi? Badhiya! Tricky sawaal yaad karo: Post 13.

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🎬 Kahani: Surbhi Ki Sale

Surbhi ki kapdon ki dukaan. Usne har kapde ka daam 50% badhaaya (cost x → 1.5x). Phir festival mein 50% discount diya. Socha: “Badhaaya 50%, ghataaya 50%, barabar! Na faayda na nuksaan.”

Mahine ke aakhir mein hisaab: sale se ₹12,000 aaye, par samaan ki laagat thi… ₹16,000! 😱 ₹4000 ka nuksaan!

Surbhi ki galti kya thi? Aaj percentage ki aisi hi aam galtiyan pakdenge.

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📖 Concept: Har Galti Ki Jad: Galat Base

Galti 1: Badhaao aur ghataao same %, wapas barabar

1.5x × 0.5 = 0.75x → 25% nuksaan! Kyun? Discount ka 50% badhe hue daam pe laga. ₹12,000 = 0.75x → x = ₹16,000, nuksaan ₹4000.

Sahi discount? 1.5x ko x pe laana: 1/1.5 = 2/3 → 33.33% discount.

Galti 2: Profit % ka base

Manisha ne ₹500 ka bag ₹750 mein becha. Profit ₹250. CP pe: 250/500 = 50%. SP pe: 250/750 = 33.33%. Jab tak alag na kaha jaaye, profit % CP pe.

Galti 3: Ek profit, ek loss, barabar SP: barabar?

Doodhwala do bhains ₹80,000-₹80,000 mein bechta: ek pe 5% profit, ek pe 10% loss. CP: 80,000/1.05 ≈ 76,190 aur 80,000/0.9 ≈ 88,889. Kul CP ≈ 1,65,079, SP 1,60,000 → ≈ ₹5,079 nuksaan (≈ 3.1%).

Galti 4: Choti % se badi ginti

100 log, 99% left-handed. Kitne left-handed jaayein ki 98% reh jaayein? “1”? Nahi! (99 − x)/(100 − x) = 0.98 → x = 50! Bache 50 mein 49 left-handed = 98%.

Galti 5: Plus-minus barabar to koi farak nahi

Chuhon ki aabaadi +5%, −2%, −3%: 5 − 2 − 3 = 0? 1.05 × 0.98 × 0.97 = 0.99813 → ≈ 0.19% kam!

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🔐 Deep Concept: Pencil Ka Raaz

“3 pencil ka SP = 5 pencil ka CP.” Faayda ya nuksaan? Ek pencil ka CP = 1 maano: 3 pencil ka SP = 5 → ek ka SP = 5/3. Profit = 2/3 per pencil → 66.67% profit.

Aur 35% markup phir 30% discount: 1.35 × 0.7 = 0.945 → 5.5% nuksaan, chahe markup discount se zyada lage! 🔐

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✏️ Solved Examples

Example 1 (Easy): Daam 20% badhaaya phir 20% ghataaya. Kul?

1.2 × 0.8 = 0.96 → 4% kam.

WHY sahi hai? ₹100 → 120 → 96 ✅

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Example 2 (Medium): Surbhi: sale se ₹12,000 aaye (1.5x pe 50% off). Laagat?

0.75x = 12,000 → x = ₹16,000, nuksaan ₹4000.

WHY sahi hai? 16,000 × 1.5 × 0.5 = 12,000 ✅

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Example 3 (NCERT style): 35% markup phir 30% discount: faayda ya nuksaan?

1.35 × 0.7 = 0.945 → 5.5% nuksaan.

WHY sahi hai? ₹100 → 135 → 94.50 ✅

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Surbhi ki seekh: “Har % se pehle poochho: kiska %?” 🎉

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🏠 Real Life Mein

🏷️ Sale ke “pehle badhaao phir ghataao” chaal.
📰 Akhbaar: “daam 50% gire, phir 50% badhe” = purana nahi!
🏪 Dukaan ka hisaab: profit CP pe.
📊 Survey: 99% → 98% ke liye aadhe log hatane pade!

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Badhaao phir ghataao same %	❌ Wapas barabar nahi	Base badla
Profit %	✅ CP pe (jab tak alag na kaha)	Default base
Wapas laane ka %	✅ 1/(1 + r) se	50% up → 33.33% down
Lagaataar ±%	✅ Guna karo	Jod nahi

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❌→✅ Worked Mistake

Sawaal: Share ₹100 ka, pehle din 50% gira, agle din 50% badha. Ab?

❌ Galat: “Wapas ₹100.”

Galti kya hai? Badhotri ₹50 pe hui ❌

✅ Sahi: 100 → 50 → 75. 25% kam!

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📝 10 MCQs

Q1. 50% up phir 50% down?

(a) 25% kam

(b) Barabar

(c) 25% zyada

(d) 50% kam

Solution dekho

Sahi jawab: (a)

(a) sahi: 0.75 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q2. Surbhi ki laagat (₹12,000 sale)?

(a) ₹16,000

(b) ₹12,000

(c) ₹18,000

(d) ₹8,000

Solution dekho

Sahi jawab: (a)

(a) sahi: 12,000/0.75 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q3. Surbhi ko kitna discount dena tha (barabar ke liye)?

(a) 33.33%

(b) 50%

(c) 25%

(d) 66.67%

Solution dekho

Sahi jawab: (a)

(a) sahi: 1 − 1/1.5 ✅
(b) galat: Galti.
(c) galat: Nahi.
(d) galat: Nahi.

Q4. ₹500 → ₹750: CP pe profit %?

(a) 50%

(b) 33.33%

(c) 25%

(d) 150%

Solution dekho

Sahi jawab: (a)

(a) sahi: 250/500 ✅
(b) galat: SP pe.
(c) galat: Nahi.
(d) galat: Nahi.

Q5. Doodhwala (5% profit, 10% loss, same SP)?

(a) ≈ ₹5,079 nuksaan

(b) Barabar

(c) Faayda

(d) ₹8,000 nuksaan

Solution dekho

Sahi jawab: (a)

(a) sahi: CP kul ≈ 1,65,079 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q6. 99% se 98% left-handed ke liye kitne jaayein?

(a) 50

(b) 1

(c) 2

(d) 49

Solution dekho

Sahi jawab: (a)

(a) sahi: (99 − x)/(100 − x) = 0.98 ✅
(b) galat: Andaaza.
(c) galat: Nahi.
(d) galat: Nahi.

Q7. +5%, −2%, −3%: kul?

(a) ≈ 0.19% kam

(b) Barabar

(c) 0.19% zyada

(d) 10% kam

Solution dekho

Sahi jawab: (a)

(a) sahi: 0.99813 ✅
(b) galat: Jod diya.
(c) galat: Nahi.
(d) galat: Nahi.

Q8. 3 pencil SP = 5 pencil CP?

(a) 66.67% profit

(b) 40% profit

(c) 40% loss

(d) Barabar

Solution dekho

Sahi jawab: (a)

(a) sahi: 5/3 − 1 ✅
(b) galat: Ulta base.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. 35% up, 30% off?

(a) 5.5% loss

(b) 5% profit

(c) Barabar

(d) 5.5% profit

Solution dekho

Sahi jawab: (a)

(a) sahi: 0.945 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q10. 20% up 20% down?

(a) 4% kam

(b) Barabar

(c) 4% zyada

(d) 40% kam

Solution dekho

Sahi jawab: (a)

(a) sahi: 0.96 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Sabse badi galti kya hai?

Base (kiska %) bhoolna.

2. Profit hamesha CP pe?

Haan, jab tak SP pe na kaha ho.

3. Ulta % kaise nikalein?

Wapas laane ke liye 1/(1 ± r).

4. 99% wala sawaal itna bada kyun?

1% = 1 aadmi tha; 2% ke liye 1 right-handed ko 50 ka 2% banna padega.

5. Jod kab theek?

Jab saare % ek hi base ke hon.

6. Galti pakadne ki trick?

₹100 maan ke ginti karo.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy ₹100, 10% up, 10% down?

Solution dekho

₹99.

Q2. Easy ₹200 CP, ₹250 SP: profit %?

Solution dekho

25%.

Q3. Easy 25% markup ko wapas laane ka discount?

Solution dekho

20%.

Q4. Easy 100% badha phir 50% ghata?

Solution dekho

Wapas barabar.

Q5. Medium ₹750 SP pe 25% profit: CP?

Solution dekho

₹600.

Q6. Medium Do cheezein ₹1200-₹1200, ek 20% profit, ek 20% loss. Kul?

Solution dekho

CP 1000 + 1500 = 2500, SP 2400 → ₹100 nuksaan.

Q7. Medium 40% markup, 25% off?

Solution dekho

1.4 × 0.75 = 1.05 → 5% profit.

Q8. NCERT style Surbhi wala: 50% markup, 50% off.

Solution dekho

25% loss; ₹12,000 sale → CP ₹16,000.

Q9. NCERT style 3 pencil SP = 5 CP.

Solution dekho

66.67% profit.

Q10. Medium Kaun sa discount (markup 25%) se barabar?

Solution dekho

20%.

Q11. Medium 200 log, 99% ek team ke. 98% ke liye kitne jaayein?

Solution dekho

100.

Q12. NCERT style 35% markup, 30% off.

Solution dekho

5.5% loss.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Kya x% up phir x% down kabhi barabar?

Solution dekho

Sirf x = 0. Warna (1 − x²/10000) → hamesha kam.

Q2. Markup m%, discount d%: barabar kab?

Solution dekho

(1 + m)(1 − d) = 1 → d = m/(1 + m).

Q3. Profit 25% CP pe = SP pe kitna?

Solution dekho

25/125 = 20%.

Q4. Kya same SP pe a% profit aur a% loss hamesha nuksaan?

Solution dekho

Haan, hamesha.

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🏆 Olympiad Corner

Q1. Same SP, 20% profit aur 20% loss: kul % nuksaan?

Solution dekho

4% (a²/100).

Q2. 10% up 3 baar phir 10% down 3 baar?

Solution dekho

(1.1 × 0.9)³ = 0.99³ ≈ 0.9703 → ≈ 2.97% kam.

Q3. Markup kitna ho ki 20% off ke baad bhi 20% profit?

Solution dekho

1.2/0.8 = 1.5 → 50%.

Q4. CP ka 120% SP, SP ka kitna % profit?

Solution dekho

20/120 = 16.67%.

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💗 CharuMam Motivation

Surbhi ne ₹4000 khoke seekha, aap ne ek post padh ke! 🕵️

Galtiyon se mat daro, unhe pakadna seekho. Jo galti ek baar samajh li, woh dobara nahi hoti. Chapter 1 poora, aur Class 8 Maths bhi! 🎓🎉

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🟢 Master Recap

Same % up phir down ≠ barabar (50% → 25% loss).
Profit % CP pe.
Same SP, profit + loss → aksar nuksaan.
99% → 98%: aadhe log hatane pade!
Har % ka base poochho; ₹100 maan ke check karo.

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👉 Aage Kya?

🎉 Chapter 1 poora! Ab Chapter 2 — Baudhayana–Pythagoras Theorem mein chalo!

← Pichla: Post 13 — Tricky Percentages 📚 Chapter 1 ke saare posts Agla chapter: Baudhayana–Pythagoras Theorem →

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

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Surbhi Ki Sale

📖 Concept: Har Galti Ki Jad: Galat Base

Galti 1: Badhaao aur ghataao same %, wapas barabar

Galti 2: Profit % ka base

Galti 3: Ek profit, ek loss, barabar SP: barabar?

Galti 4: Choti % se badi ginti

Galti 5: Plus-minus barabar to koi farak nahi

🔐 Deep Concept: Pencil Ka Raaz

✏️ Solved Examples

🏠 Real Life 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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