Tricky Percentages | Class 8 Maths Book 2 Ch 1 (Fractions in Disguise)

📘 Class 8 · Ganita Prakash Book 2Ch 1 · Fractions in DisguisePost 13 / 14⏱ 25–30 min

Tricky Percentages 🧩

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:

₹200 ka 30%?
₹140 ka 20%?
5% of 40 = ?

Answers dekho

₹60
₹28
2

Teeno sahi? Badhiya! Profit-loss yaad karo: Post 9.

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🎬 Kahani: Do Cake Ki Dukaanein

Priya ka janamdin! ₹200 ka cake lena tha. Cakely dukaan: “30% + 20% off!” Cakify: “50% off!”

Rohan: “Dono same, 30 + 20 = 50!” Priya ne hisaab lagaaya: Cakely: 200 → 140 → 112. Cakify: 100. 🎂

Farak ₹12 ka! Percentage kabhi-kabhi dhokha deta hai. Aaj aise hi tricky sawaalon ko pakadna seekhenge.

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📖 Concept: Base Pe Dhyaan Do

Step 1: Lagaataar discount jodte nahi

30% off → 0.7, phir 20% off → 0.8. Kul = 0.7 × 0.8 = 0.56 → 44% off, 50% nahi.

WHY? Doosra 20% ghate hue daam (₹140) pe laga, ₹200 pe nahi.

Step 2: Lagaataar badhotri bhi

Bus kiraya pichhle saal 3%, is saal 4% badha. Kul = 1.03 × 1.04 = 1.0712 → 7.12%, 7% nahi.

Step 3: % zyada vs rakam zyada

A: ₹100 do, ₹300 lo (200% faayda). B: ₹1000 do, ₹1500 lo (50% faayda). % mein A behtar, par rakam mein B (₹500 vs ₹200)! Kaunsa chunein, yeh aapke paas kitna paisa hai, us pe nirbhar.

Step 4: “₹50 off” ya “20% off”?

Kharid ₹150 se upar: 20% off = ₹50 kab? 0.2 × x = 50 → x = ₹250. ₹250 se kam (jaise 180, 225) → ₹50 off behtar. ₹250 se zyada (jaise 300) → 20% off behtar.

Step 5: Ulti tulna

Ariba ke paas Arun ke 120% kanche. Arun ke paas Ariba ke kitne? 1 ÷ 1.2 = 83.33% (100% − 20% nahi!). Arun keh sakta: “Mere paas tumse 16.67% kam hain.”

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🔐 Deep Concept: x% of y = y% of x

5% of 40 = 2 aur 40% of 5 = 2. 25% of 12 = 3 aur 12% of 25 = 3. Hamesha barabar!

Algebra: x% of y = (x/100) × y = xy/100 = (y/100) × x = y% of x ✅

Trick: 16% of 25 mushkil? 25% of 16 = 4! Mental maths ka shortcut. 🔐

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✏️ Solved Examples

Example 1 (Easy): ₹500 pe 20% + 10% off. Daam?

500 × 0.8 × 0.9 = ₹360 (28% off).

WHY sahi hai? 30% seedha hota to ₹350 ✅

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Example 2 (Medium): Rectangle ki lambaai 10% badhi, area same. Chaudaai kitne % ghati?

Chaudaai × 1/1.1 = 0.909… → 9.09% (1/11) ghati.

WHY sahi hai? 1.1 × 0.909 = 1 ✅

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Example 3 (NCERT style): Trip ke 40% bachche Grade 8 ke, unme 60% ladkiyaan. Kul ke kitne % Grade 8 ladkiyaan? 250 bachche hon to kitni?

0.4 × 0.6 = 0.24 → 24%. 250 ka 24% = 60.

WHY sahi hai? % ka %: guna ✅

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Priya ka mantra: “Har % ka base poochho: kiska %?” 🎉

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🏠 Real Life Mein

🛍️ Sale: “Flat 50%” vs “30% + 20%”.
🚌 Kiraya/daam saal-dar-saal.
🏦 Investment: % aur rakam dono dekho.
🎁 Buy 1 Get 1 jaise offers.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Lagaataar % badlaav	✅ Guna karo	Base badalta
30% + 20% = 50%	❌ Galat	44%
Ulti tulna (A, B ka 120%)	✅ 1 ÷ 1.2	83.33%
x% of y mushkil	✅ y% of x try karo	Barabar

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❌→✅ Worked Mistake

Sawaal: Ariba ke paas Arun ke 120%. Arun ke paas Ariba ke kitne %?

❌ Galat: “80%.”

Galti kya hai? Base badal gaya (ab Ariba) ❌

✅ Sahi: 100 ÷ 120 = 83.33%. Jaise Arun 10, Ariba 12: 10/12 = 83.33%.

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📝 10 MCQs

Q1. Cakely (30% + 20%) pe ₹200 cake?

(a) ₹112

(b) ₹100

(c) ₹140

(d) ₹120

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Cakify.
(c) galat: Sirf 30%.
(d) galat: Nahi.

Q2. 30% + 20% lagaataar = kul?

(a) 44%

(b) 50%

(c) 56%

(d) 6%

Solution dekho

Sahi jawab: (a)

(a) sahi: 1 − 0.56 ✅
(b) galat: Jod diya.
(c) galat: Bacha hissa.
(d) galat: Nahi.

Q3. Bus 3% phir 4%?

(a) 7.12%

(b) 7%

(c) 12%

(d) 1%

Solution dekho

Sahi jawab: (a)

(a) sahi: 1.0712 ✅
(b) galat: Jod.
(c) galat: Guna kiye % ko.
(d) galat: Nahi.

Q4. 20% off ₹50 ke barabar kab?

(a) ₹250

(b) ₹200

(c) ₹300

(d) ₹150

Solution dekho

Sahi jawab: (a)

(a) sahi: 50 ÷ 0.2 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q5. ₹225 kharid: behtar?

(a) ₹50 off

(b) 20% off

(c) Barabar

(d) Pata nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: 20% = ₹45 ✅
(b) galat: Kam.
(c) galat: Nahi.
(d) galat: Pata hai.

Q6. ₹300: behtar?

(a) 20% off

(b) ₹50 off

(c) Barabar

(d) Koi nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: ₹60 > ₹50 ✅
(b) galat: Kam.
(c) galat: Nahi.
(d) galat: Nahi.

Q7. Ariba 120% → Arun Ariba ka?

(a) 83.33%

(b) 80%

(c) 120%

(d) 20%

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Base galat.
(c) galat: Ulta.
(d) galat: Nahi.

Q8. 16% of 25?

(a) 4

(b) 16

(c) 25

(d) 0.4

Solution dekho

Sahi jawab: (a)

(a) sahi: 25% of 16 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. Lambaai +10%, area same: chaudaai?

(a) −9.09%

(b) −10%

(c) −11%

(d) Same

Solution dekho

Sahi jawab: (a)

(a) sahi: 1/11 ✅
(b) galat: Andaaza.
(c) galat: Nahi.
(d) galat: Nahi.

Q10. 40% ka 60%?

(a) 24%

(b) 100%

(c) 20%

(d) 36%

Solution dekho

Sahi jawab: (a)

(a) sahi: 0.4 × 0.6 ✅
(b) galat: Jod.
(c) galat: Farak.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Lagaataar discount ka shortcut?

Bache hisse guna karo: 0.7 × 0.8.

2. % faayda zyada matlab hamesha behtar?

Nahi, rakam bhi dekho.

3. % of % kaise?

Guna.

4. “% kam” ka ulta?

Bada % badhaana padta (10% kam → 11.1% badhao).

5. Buy 1 Get 1 = kitna discount?

50%.

6. Buy 2 Get 1?

3 ke 2 ka daam → 33.33% off.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy 25% of 12 aur 12% of 25?

Solution dekho

Dono 3.

Q2. Easy ₹1000 pe 10% + 10% off?

Solution dekho

₹810.

Q3. Easy Buy 1 Get 1 (₹100 item): har ek?

Solution dekho

₹50.

Q4. Easy 15% of 60 aur 60% of 15?

Solution dekho

Dono 9.

Q5. Medium Buy 2 Get 1 aur Buy 3 Get 1: har item?

Solution dekho

₹66.67 aur ₹75.

Q6. Medium Teen dukaanein (B1G1, B2G1, B3G1): sasta se mehenga?

Solution dekho

A, B, C (50%, 33.33%, 25% off).

Q7. Medium Bengaluru 2000 mein 50 lakh, 2025 mein 250%. 2025?

Solution dekho

1.25 crore.

Q8. NCERT style ₹180, ₹225, ₹300: ₹50 off ya 20% off?

Solution dekho

₹50, ₹50, 20%.

Q9. NCERT style Cakely vs Cakify.

Solution dekho

₹112 vs ₹100.

Q10. Medium A: ₹100 → ₹300, B: ₹1000 → ₹1500. % faayda?

Solution dekho

200% vs 50%.

Q11. Medium Daam 25% badha, kitne % ghataayein to wapas?

Solution dekho

1/1.25 = 0.8 → 20%.

Q12. NCERT style 4 item lene ho to kaunsi dukaan (B3G1 ya B1G1)?

Solution dekho

B1G1: 4 ke 2 ka daam (₹200) sasta.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Do lagaataar 50% off = ?

Solution dekho

75% off (0.25 bacha).

Q2. Kya 3 baar 10% badhna 1 baar 30% se zyada?

Solution dekho

1.331 > 1.3, haan.

Q3. Kaun bada: 30% of 70 ya 70% of 30?

Solution dekho

Barabar (21).

Q4. Daam 20% badha phir 20% ghata. Kul?

Solution dekho

4% kam.

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🏆 Olympiad Corner

Q1. Lagaataar a% aur b% badhotri ka kul?

Solution dekho

a + b + ab/100 %.

Q2. Area same, lambaai 25% badhi. Chaudaai?

Solution dekho

1/1.25 = 0.8 → 20% kam.

Q3. Kitne lagaataar 10% discount se daam aadha?

Solution dekho

0.9⁶ ≈ 0.53, 0.9⁷ ≈ 0.48 → 7.

Q4. x ka 20% = y ka 30%. x : y?

Solution dekho

0.2x = 0.3y → 3 : 2.

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💗 CharuMam Motivation

Priya ne “50%” ke jaadu mein na phas ke hisaab lagaaya aur ₹12 bachaaye! 🎂

Duniya mein bahut offers aur daave aate hain. Ganit aapko samajhdaar grahak aur samajhdaar insaan banata hai. Hamesha hisaab lagao! 🧠

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🟢 Master Recap

Lagaataar % badlaav guna hote: 30% + 20% off = 44% off.
3% phir 4% = 7.12%.
% aur rakam dono dekho.
Ulti tulna: 120% → 83.33%.
x% of y = y% of x.

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👉 Aage Kya?

Chapter ka aakhri post! Sabse aam percentage ki galtiyan: 50% badhaa ke 50% ghataaya to wapas barabar? Pakdo galti! 🕵️

← Pichla: Post 12 — Depreciation 📚 Chapter 1 ke saare posts Agla: Post 14 — Percentage Ki Galtiyan Pakdo →

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

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Do Cake Ki Dukaanein

📖 Concept: Base Pe Dhyaan Do

Step 1: Lagaataar discount jodte nahi

Step 2: Lagaataar badhotri bhi

Step 3: % zyada vs rakam zyada

Step 4: “₹50 off” ya “20% off”?

Step 5: Ulti tulna

🔐 Deep Concept: x% of y = y% of x

✏️ 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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