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

📘 Class 8 · Ganita Prakash Book 2Ch 1 · Fractions in DisguisePost 12 / 14⏱ 25–30 min

Depreciation 📉

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:

₹21,000 ka 5%?
100% − 5% = ?
0.9 × 0.9 = ?

Answers dekho

₹1050
95%
0.81

Teeno sahi? Badhiya! Compounding yaad karo: Post 11 — Growth aur Compounding.

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🎬 Kahani: Papa Ka Purana TV

Papa ne ₹21,000 ka TV khareeda tha. Ek saal baad unhone use bechne ka socha. Dukaandaar bola: “Ab yeh ₹19,950 ka hai.”

Golu naraaz: “TV to bilkul theek hai! Keemat kam kyun?” Papa ne samjhaaya: “Beta, istemaal aur umar ke saath cheezon ki keemat girti hai. Ise depreciation kehte hain.” 📺

Kitne % giri? Aur agle saal kitni girega? Chalo dekhte hain!

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📖 Concept: Har Saal (1 − r) Se Guna

Step 1: Depreciation kya hai?

Umar aur istemaal se kisi cheez ki value ka kam hona: gaadi, phone, machine, TV.

Step 2: Ek saal

TV ₹21,000, 5% depreciation: kami = 5% × 21,000 = ₹1050. Nayi value = ₹19,950. Ya seedha: 95% × 21,000 = 0.95 × 21,000 = 19,950.

WHY 95%? 5% gaya, 95% bacha. “5% ghataao” = “0.95 se guna karo”.

Step 3: Kai saal: baar-baar guna

Har saal ghatti hui nayi value pe hi % lagta (compounding jaisa, par ulta):

Value = p(1 − r)ᵗ

Step 4: Gaon ki aabaadi

Gaon mein 1250 log, har dashak (10 saal) 10% kam. 1250 → 1125 → 1012.5 (≈ 1013) → 911.25 (≈ 912). Teen dashak baad lagbhag 910.

1250 × 0.9 × 0.9 × 0.9 = 1250 × 0.729 = 911.25 ✅

WHY 30% nahi ghata? 3 × 10% = 30% ghata hota to 875 bachte. Par har baar 10% chhote number ka, to kul kami 27.1% hi.

Step 5: Growth vs decline

Growth: × (1 + r) baar-baar. Decline: × (1 − r) baar-baar. Ek hi soch, ulti disha!

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🔐 Deep Concept: Kabhi Zero Nahi Hota

Har saal 10% kam: 0.9, 0.81, 0.729… value chhoti hoti jaati par kabhi zero nahi. (Ch 4 ke fractals jaisa: (8/9)ⁿ!)

Isliye companies kabhi-kabhi doosra tareeka bhi use karti: har saal same rakam kam (seedhi line), taaki kuch saal mein value zero (ya scrap value) ho jaaye. Do tareeke, do kahaniyaan. 🔐

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✏️ Solved Examples

Example 1 (Easy): Phone ₹15,000, 20% depreciation, 1 saal?

0.8 × 15,000 = ₹12,000.

WHY sahi hai? ₹3000 kam = 20% ✅

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Example 2 (Medium): Usi phone ki 2 saal baad value?

15,000 × 0.8 × 0.8 = 15,000 × 0.64 = ₹9,600.

WHY sahi hai? Doosre saal ₹2400 kam (₹12,000 ka 20%) ✅

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Example 3 (NCERT style): Gaon 1250, har dashak 10% kam. 2 dashak baad?

1250 × 0.81 = 1012.5 ≈ 1013.

WHY sahi hai? 1125 ka 10% = 112.5 kam ✅

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Papa ka mantra: “Ghatna ho to (1 − r) se guna, baar-baar!” 🎉

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🏠 Real Life Mein

🚗 Gaadi: naye se purani hote hi keemat giri.
📱 Phone/laptop: naya model aate hi purane ki value giri.
🏭 Machinery: businesses har saal depreciation ka hisaab rakhte.
🏘️ Gaon se pravaas: aabaadi % se ghatna.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Har saal % se kam	✅ p(1 − r)ᵗ	Naye value pe %
Teen saal 10% = 30% kam	❌ Galat	27.1% kam
Ek saal	✅ (1 − r) × p	95% bacha
Same rakam har saal kam	✅ Seedhi line (alag tareeka)	Linear

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❌→✅ Worked Mistake

Sawaal: Bike ₹50,000, har saal 10% depreciation. 2 saal baad?

❌ Galat: “20% kam → ₹40,000.”

Galti kya hai? Doosre saal 10% ₹45,000 ka lagta ❌

✅ Sahi: 50,000 × 0.81 = ₹40,500.

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📝 10 MCQs

Q1. TV ₹21,000, 5%, 1 saal?

(a) ₹19,950

(b) ₹20,000

(c) ₹1050

(d) ₹22,050

Solution dekho

Sahi jawab: (a)

(a) sahi: 0.95 × 21,000 ✅
(b) galat: Andaaza.
(c) galat: Kami.
(d) galat: Badha diya.

Q2. Depreciation formula?

(a) p(1 − r)ᵗ

(b) p(1 + r)ᵗ

(c) p − rt

(d) prt

Solution dekho

Sahi jawab: (a)

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

Q3. 10% kam = kis se guna?

(a) 0.9

(b) 0.1

(c) 1.1

(d) 10

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Kami ka hissa.
(c) galat: Badhna.
(d) galat: Nahi.

Q4. Gaon 1250, 3 dashak 10%?

(a) ≈ 911

(b) 875

(c) 1125

(d) 1000

Solution dekho

Sahi jawab: (a)

(a) sahi: 1250 × 0.729 ✅
(b) galat: 30% seedha ghata diya.
(c) galat: Ek dashak.
(d) galat: Nahi.

Q5. 3 baar 10% kam = kul?

(a) 27.1%

(b) 30%

(c) 33.1%

(d) 10%

Solution dekho

Sahi jawab: (a)

(a) sahi: 1 − 0.729 ✅
(b) galat: Nahi.
(c) galat: Growth ka.
(d) galat: Nahi.

Q6. Phone ₹15,000, 20%, 2 saal?

(a) ₹9,600

(b) ₹9,000

(c) ₹12,000

(d) ₹6,000

Solution dekho

Sahi jawab: (a)

(a) sahi: × 0.64 ✅
(b) galat: 40% seedha.
(c) galat: Ek saal.
(d) galat: Nahi.

Q7. Kya value kabhi zero (% wale tareeke se)?

(a) Nahi

(b) Haan, 10 saal mein

(c) Haan, turant

(d) Pata nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Hamesha thoda bachta ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Pata hai.

Q8. Bike ₹50,000, 10%, 2 saal?

(a) ₹40,500

(b) ₹40,000

(c) ₹45,000

(d) ₹41,000

Solution dekho

Sahi jawab: (a)

(a) sahi: × 0.81 ✅
(b) galat: Seedha 20%.
(c) galat: Ek saal.
(d) galat: Nahi.

Q9. Depreciation kyun?

(a) Umar aur istemaal

(b) Mehngaai

(c) Tax

(d) Byaaj

Solution dekho

Sahi jawab: (a)

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

Q10. 20% kam phir 20% badha (₹100)?

(a) ₹96

(b) ₹100

(c) ₹104

(d) ₹80

Solution dekho

Sahi jawab: (a)

(a) sahi: 100 × 0.8 × 1.2 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Depreciation aur discount mein farak?

Discount dukaandaar deta; depreciation umar se value girna.

2. Har cheez depreciate hoti?

Nahi; zameen, sona aksar badhte (appreciate).

3. Aabaadi pe depreciation?

Shabd “decline”; formula wahi.

4. Rounding?

Logon ki ginti poori: 1012.5 ≈ 1013.

5. Kya rate badal sakta?

Haan; har saal alag rate se guna karo.

6. Seedhi line wala?

Har saal fixed rakam kam; aage padhoge.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy ₹10,000, 10%, 1 saal?

Solution dekho

₹9,000.

Q2. Easy ₹10,000, 10%, 2 saal?

Solution dekho

₹8,100.

Q3. Easy 5% kam ka guna?

Solution dekho

0.95.

Q4. Easy Car ₹5,00,000, 15%, 1 saal?

Solution dekho

₹4,25,000.

Q5. Medium Machine ₹80,000, 25%, 2 saal?

Solution dekho

80,000 × 0.5625 = ₹45,000.

Q6. Medium Aabaadi 20,000, 5% saalana kam, 2 saal?

Solution dekho

20,000 × 0.9025 = 18,050.

Q7. Medium Value 1 saal baad ₹27,000, rate 10%. Shuru?

Solution dekho

27,000 ÷ 0.9 = ₹30,000.

Q8. NCERT style TV ₹21,000, 5% depreciation.

Solution dekho

₹19,950.

Q9. NCERT style Gaon 1250, 10%/dashak, teen dashak.

Solution dekho

≈ 911 (lagbhag 910).

Q10. Medium Laptop ₹60,000, 2 saal mein ₹48,600. Rate?

Solution dekho

48,600 ÷ 60,000 = 0.81 → 10%.

Q11. Medium Kitne % kul kami (20% do baar)?

Solution dekho

1 − 0.64 = 36%.

Q12. NCERT style Growth aur decline formula mein farak?

Solution dekho

(1 + r) vs (1 − r).

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🧠 HOTS (Sochne Wale Sawaal)

Q1. 10% kam phir 10% badhe: wapas same?

Solution dekho

0.9 × 1.1 = 0.99 → 1% kam.

Q2. Value aadhi kab (10% saalana)?

Solution dekho

0.9⁶ ≈ 0.53, 0.9⁷ ≈ 0.48 → 7 saal mein aadhi se kam.

Q3. 50% do baar kam vs 100% ek baar?

Solution dekho

0.25 bacha vs 0 bacha.

Q4. Rate double karne se kami double?

Solution dekho

Pehle saal haan, baad mein nahi.

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🏆 Olympiad Corner

Q1. Car 3 saal mein ₹7,29,000, 10% saalana. Shuru?

Solution dekho

7,29,000 ÷ 0.729 = ₹10,00,000.

Q2. Kab value 1/4 se kam (20% saalana)?

Solution dekho

0.8⁶ ≈ 0.26, 0.8⁷ ≈ 0.21 → 7 saal.

Q3. Pehle saal 20%, doosre 10% kam: kul?

Solution dekho

0.8 × 0.9 = 0.72 → 28%.

Q4. Aabaadi 10% kam phir kitne % badhe to wapas?

Solution dekho

1/0.9 ≈ 1.111 → 11.1%.

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💗 CharuMam Motivation

TV ki value giri, par uski yaadein nahi! 📺

Cheezon ki keemat ghatti hai, par gyaan ki keemat har saal badhti hai. Isliye cheezon se zyada seekhne mein nivesh karo! 📚

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🟢 Master Recap

Depreciation = umar/istemaal se value kam.
Ek saal: × (1 − r) (5% kam = × 0.95).
Kai saal: p(1 − r)ᵗ.
3 baar 10% kam = 27.1% kam (30% nahi).
Growth × (1 + r), decline × (1 − r).

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👉 Aage Kya?

Ab dimaag ghumaane wale sawaal: 30% + 20% discount = 50%? 120% kya hai? Agle post mein Tricky Percentages! 🧩

← Pichla: Post 11 — Growth aur Compounding 📚 Chapter 1 ke saare posts Agla: Post 13 — Tricky Percentages →

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

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Papa Ka Purana TV

📖 Concept: Har Saal (1 − r) Se Guna

Step 1: Depreciation kya hai?

Step 2: Ek saal

Step 3: Kai saal: baar-baar guna

Step 4: Gaon ki aabaadi

Step 5: Growth vs decline

🔐 Deep Concept: Kabhi Zero Nahi Hota

✏️ 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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