Growth aur Compounding | Class 8 Maths Book 2 Ch 1 (Fractions in Disguise)

📘 Class 8 · Ganita Prakash Book 2Ch 1 · Fractions in DisguisePost 11 / 14⏱ 25–30 min

Growth aur Compounding 📈

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:

₹6000 ka 10%?
₹6600 ka 10%?
1.1 × 1.1 = ?

Answers dekho

₹600
₹660
1.21

Teeno sahi? Badhiya! Percentage increase yaad karna ho to Post 8 — Percentage Increase aur Decrease dekh lijiye.

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🎬 Kahani: Dadi Ki Gullak Aur Bank

Golu ki Dadi ne ₹6000 bank mein 10% saalana byaaj (interest) pe 3 saal ke liye rakhe. Bank wale bhaiya ne do vikalp diye:

Vikalp A: Har saal ₹600 byaaj aapko de denge. Vikalp B: Byaaj aapke paise mein jodte jaayenge, aur agle saal byaaj naye, bade paise pe lagega.

Golu bola, “Dono mein 10% hi to hai, farak kya?” Dadi muskuraayi: “Beta, B mein byaaj pe bhi byaaj milta hai!” Aaj dekhte hain kitna farak padta hai. 💰

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📖 Concept: Byaaj Pe Byaaj

Step 1: Shabd

Principal (p): jo paisa shuru mein rakha.
Rate (r): saalana byaaj ka percentage.
Time (t): kitne saal.

Step 2: Simple interest (bina compounding)

Har saal byaaj sirf shuru ke paise pe: ₹6000 ka 10% = ₹600 har saal. 3 saal: ₹1800 byaaj, kul ₹7800.

Amount = p(1 + rt)

r ko decimal mein (10% = 0.1): 6000 × (1 + 0.1 × 3) = 6000 × 1.3 = 7800 ✅

Step 3: Compound interest (compounding)

Byaaj jud-jud ke naya principal banta: ₹6000 → 6600 (+600) → 7260 (+660) → 7986 (+726).

Amount = p(1 + r)ᵗ

6000 × 1.1 × 1.1 × 1.1 = 6000 × 1.331 = 7986 ✅

WHY bada? Doosre saal ₹600 ke byaaj pe bhi ₹60 byaaj mila, teesre saal aur zyada. Har saal “10% badhaao” = “1.1 se guna karo”.

Step 4: Kul faayda percentage mein

Simple: 7800 ÷ 6000 = 130% → 30% badha. Compound: 7986 ÷ 6000 = 133.1% → 33.1% badha.

Step 5: Linear vs exponential

Simple mein har saal same badhotri (₹600, ₹600, ₹600): seedhi line (linear). Compound mein badhotri khud badhti (600, 660, 726…): tezi se upar (exponential). Lambe samay mein farak bahut bada!

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🔐 Deep Concept: Paisa Double Kab Hoga?

₹1000, 10% saalana. Simple: har saal ₹100 → double (₹2000) 10 saal mein. Compound: 1.1⁷ ≈ 1.95, 1.1⁸ ≈ 2.14 → 8 saal se pehle hi double (7 saal ke thoda baad)!

Ek chhoti trick (“Rule of 72”): 72 ÷ rate ≈ double hone ke saal. 72 ÷ 10 = 7.2 saal. Bilkul paas! 🔐

Yahi compounding aabaadi, bacteria aur karz (loan) mein bhi hoti hai. Karz pe compounding ulta nuksaan karti hai!

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✏️ Solved Examples

Example 1 (Easy): ₹20,000, 10% saalana, 2 saal. Simple aur compound amount?

Simple: 20,000 × 1.2 = ₹24,000. Compound: 20,000 × 1.21 = ₹24,200.

WHY sahi hai? Compound ₹200 zyada (₹2000 ke byaaj pe 10%) ✅

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Example 2 (Medium): ₹20,000, 5% saalana, 4 saal?

Simple: 20,000 × 1.2 = ₹24,000. Compound: 20,000 × 1.05⁴ = 20,000 × 1.21550625 ≈ ₹24,310.

WHY sahi hai? Same simple, par compound alag: kam rate, zyada saal mein bhi compounding ka asar ✅

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Example 3 (NCERT style): Shehar ki aabaadi 1.5 crore, har saal 3% badhti. 3 saal baad?

1.5 × 1.03³ = 1.5 × 1.092727 ≈ 1.639 crore (lagbhag 1,63,90,905).

WHY sahi hai? Har saal × 1.03 ✅

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Dadi ka mantra: “Har saal × (1 + r), aur dekho paisa kaise badhta!” 🎉

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🏠 Real Life Mein

🏦 Bank FD, post office ki bachat.
💳 Loan aur credit card: karz pe compounding, isliye jaldi chukaao.
👪 Aabaadi har saal % se badhna.
🦠 Bacteria har ghante % se badhna.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Byaaj sirf shuru ke paise pe	✅ p(1 + rt)	Simple interest
Byaaj judta jaaye	✅ p(1 + r)ᵗ	Compound
10% teen saal = 30% compound mein	❌ Galat	33.1%
Aabaadi/bacteria badhna	✅ Compound jaisa	Har baar naye number pe

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❌→✅ Worked Mistake

Sawaal: ₹10,000, 10% compound, 2 saal. Amount?

❌ Galat: “10% + 10% = 20% → ₹12,000.”

Galti kya hai? Doosre saal ka 10% ₹11,000 pe lagta hai, ₹10,000 pe nahi ❌

✅ Sahi: 10,000 × 1.1 × 1.1 = ₹12,100.

Yaad rakho: Compound mein percentage guna hote hain, jodte nahi.

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📝 10 MCQs

Q1. ₹6000, 10%, 3 saal simple amount?

(a) ₹7800

(b) ₹7986

(c) ₹6600

(d) ₹1800

Solution dekho

Sahi jawab: (a)

(a) sahi: 6000 × 1.3 ✅
(b) galat: Compound.
(c) galat: Ek saal.
(d) galat: Sirf byaaj.

Q2. Usi ka compound?

(a) ₹7986

(b) ₹7800

(c) ₹7260

(d) ₹8000

Solution dekho

Sahi jawab: (a)

(a) sahi: 6000 × 1.331 ✅
(b) galat: Simple.
(c) galat: Do saal.
(d) galat: Andaaza.

Q3. Compound formula?

(a) p(1 + r)ᵗ

(b) p(1 + rt)

(c) prt

(d) p + r + t

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Simple.
(c) galat: Sirf simple byaaj.
(d) galat: Nahi.

Q4. ₹10,000, 10% compound 2 saal?

(a) ₹12,100

(b) ₹12,000

(c) ₹11,000

(d) ₹12,200

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Simple.
(c) galat: Ek saal.
(d) galat: Nahi.

Q5. Compound 3 saal 10% = kul kitna % faayda?

(a) 33.1%

(b) 30%

(c) 31%

(d) 10%

Solution dekho

Sahi jawab: (a)

(a) sahi: 1.331 ✅
(b) galat: Simple.
(c) galat: Nahi.
(d) galat: Nahi.

Q6. ₹1000, 10% simple, double kab?

(a) 10 saal

(b) 7 saal

(c) 8 saal

(d) 5 saal

Solution dekho

Sahi jawab: (a)

(a) sahi: Har saal ₹100 ✅
(b) galat: Compound ke paas.
(c) galat: Compound.
(d) galat: Nahi.

Q7. Compound mein ₹1000 double lagbhag?

(a) 8 saal se pehle (7+)

(b) 10 saal

(c) 5 saal

(d) 20 saal

Solution dekho

Sahi jawab: (a)

(a) sahi: 1.1⁸ ≈ 2.14 ✅
(b) galat: Simple.
(c) galat: Nahi.
(d) galat: Nahi.

Q8. Simple interest ka graph?

(a) Seedhi line (linear)

(b) Curve

(c) Gol

(d) Seedha neeche

Solution dekho

Sahi jawab: (a)

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

Q9. 3% saalana badhne ka guna?

(a) 1.03

(b) 1.3

(c) 0.03

(d) 3

Solution dekho

Sahi jawab: (a)

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

Q10. ₹20,000, 10%, 2 saal: compound − simple?

(a) ₹200

(b) ₹2000

(c) ₹0

(d) ₹420

Solution dekho

Sahi jawab: (a)

(a) sahi: 24,200 − 24,000 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Byaaj kya hai?

Paisa rakhne/udhaar dene ka kiraya, percentage mein.

2. Banks compound kyun dete?

Aksar FD mein byaaj judta rehta (kai baar saal mein ek se zyada baar bhi).

3. r decimal mein kyun?

10% = 10/100 = 0.1; formula mein decimal lagta.

4. Loan pe compound?

Haan, isliye karz jaldi badhta; sambhal ke lo.

5. Rule of 72 pakka?

Andaaza hai, chhote rates pe achha kaam karta.

6. Aabaadi pe bhi same formula?

Haan, p(1 + r)ᵗ.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy ₹5000, 8% simple, 2 saal: byaaj?

Solution dekho

₹800.

Q2. Easy ₹5000, 10% compound, 1 saal?

Solution dekho

₹5500.

Q3. Easy ₹5000, 10% compound, 2 saal?

Solution dekho

₹6050.

Q4. Easy 5% badhne ka guna?

Solution dekho

1.05.

Q5. Medium ₹50,000, 7%, 3 saal: simple byaaj aur compound kitna zyada?

Solution dekho

Simple ₹10,500. Compound amount ≈ ₹61,252.15 → byaaj ₹11,252.15, yaani ≈ ₹752 zyada.

Q6. Medium Giridhar ₹12,500 pe 12% simple 3 saal; Raghava 10% compound. Kaun zyada chukaata?

Solution dekho

Giridhar ₹17,000, Raghava ₹16,637.50 → Giridhar ₹362.50 zyada.

Q7. Medium Bacteria 5,06,000, 2.5% har ghanta, 2 ghante?

Solution dekho

5,06,000 × 1.050625 ≈ 5,31,616.

Q8. NCERT style ₹20,000: 10% 2 saal vs 5% 4 saal, compound?

Solution dekho

₹24,200 vs ≈ ₹24,310.

Q9. NCERT style Kya compounding exponential aur simple linear?

Solution dekho

Haan.

Q10. Medium Jasmine p, 6%, 4 saal bina compounding: amount?

Solution dekho

p(1 + 0.24) = 1.24p.

Q11. Medium Aabaadi 10,000, 10% saalana, 2 saal?

Solution dekho

12,100.

Q12. NCERT style ₹1000, 10%: double kab (dono tareeke)?

Solution dekho

Simple 10 saal; compound 7 aur 8 saal ke beech.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. ₹100, 100% saalana compound, 3 saal?

Solution dekho

100 → 200 → 400 → 800.

Q2. Kya compound kabhi simple se kam?

Solution dekho

Pehle saal barabar; baad mein hamesha zyada (positive rate pe).

Q3. Do bank: 10% simple vs 9% compound, 10 saal. Kaun behtar?

Solution dekho

Simple: 2× ; compound 1.09¹⁰ ≈ 2.37× → compound behtar.

Q4. Saal mein do baar 5% (har 6 mahine) vs ek baar 10%?

Solution dekho

1.05² = 1.1025 > 1.1 → do baar behtar.

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🏆 Olympiad Corner

Q1. Kitne saal mein ₹1000, 20% compound se ₹2000 se zyada?

Solution dekho

1.2⁴ ≈ 2.07 → 4 saal.

Q2. Compound amount 2 saal ₹14,520, 3 saal ₹15,972. Rate?

Solution dekho

15,972 ÷ 14,520 = 1.1 → 10%.

Q3. Usi ka principal?

Solution dekho

14,520 ÷ 1.21 = ₹12,000.

Q4. Aabaadi 20% badhi phir 20% ghati. Kul?

Solution dekho

1.2 × 0.8 = 0.96 → 4% kam.

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💗 CharuMam Motivation

Dadi ke paise ne sikhaaya: chhoti-chhoti badhotri, lagaataar, bahut bada fark laati hai. 💰

Padhaai bhi compound interest jaisi hai! Roz ka thoda sa gyaan kal ke gyaan pe judta hai. Aaj 1% behtar, saal bhar mein kamaal! 📈

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🟢 Master Recap

Simple: byaaj sirf shuru ke paise pe: p(1 + rt).
Compound: byaaj pe byaaj: p(1 + r)ᵗ.
₹6000, 10%, 3 saal: 7800 vs 7986.
Compound mein % guna hote, jodte nahi.
Simple = linear, compound = exponential.

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👉 Aage Kya?

Agar har saal value ghatti jaaye? Gaadi, phone, TV ki keemat kyun girti hai? Agle post mein Depreciation! 📉

← Pichla: Post 10 — Tax (GST)📚 Chapter 1 ke saare posts Agla: Post 12 — Depreciation →

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

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Dadi Ki Gullak Aur Bank

📖 Concept: Byaaj Pe Byaaj

Step 1: Shabd

Step 2: Simple interest (bina compounding)

Step 3: Compound interest (compounding)

Step 4: Kul faayda percentage mein

Step 5: Linear vs exponential

🔐 Deep Concept: Paisa Double Kab Hoga?

✏️ 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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