Class 10 Mathematics | Unit 3 Growth and Depreciation Formula & Key Points
Introduction to the Chapter
Welcome to the essential guide for Unit 3 Growth and Depreciation (वृद्धि र ह्रास). This unit applies compound interest concepts to real-world scenarios like population growth and the depreciation of assets.
संकेतहरू (Notations):
- $P$ वा $P_0 =$ सुरुको जनसङ्ख्या वा मूल्य (Initial Population/Price)
- $P_T =$ $T$ वर्षपछिको जनसङ्ख्या वा मूल्य (Population/Price after $T$ years)
- $R =$ वृद्धि वा ह्रास दर प्रतिवर्ष (Rate of growth/depreciation)
- $T =$ समय (Time in years)
1. जनसङ्ख्या वृद्धि (Population Growth)
| अवस्था (Condition) | सूत्र (Formula) |
|---|---|
|
साधारण वृद्धि हुँदा General Growth |
$$P_T = P\left(1+\frac{R}{100}\right)^T$$
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|
हरेक वर्षको वृद्धिदर फरक-फरक Different rates $R_1, R_2…$ |
$$P_T = P\left(1+\frac{R_1}{100}\right)\left(1+\frac{R_2}{100}\right)…$$
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|
वर्ष र महिनामा समय हुँदा Time in Years & Months |
$$P_T = P\left(1+\frac{R}{100}\right)^T \left(1+\frac{MR}{1200}\right)$$
|
2. मिश्रित ह्रास (Compound Depreciation)
प्रयोग हुने: मेसिन, गाडी वा सम्पत्तिको मूल्य घट्दा (Used for: Depreciation of machines, vehicles, assets).
| अवस्था (Condition) | सूत्र (Formula) |
|---|---|
|
साधारण ह्रास हुँदा General Depreciation |
$$P_T = P\left(1-\frac{R}{100}\right)^T$$
|
|
हरेक वर्षको ह्रास दर फरक-फरक Different rates |
$$P_T = P\left(1-\frac{R_1}{100}\right)\left(1-\frac{R_2}{100}\right)…$$
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3. Important Relations (महत्त्वपूर्ण सम्बन्धहरू)
Migration & Vital Events
Final Population =
$$P_{initial} + \text{Births} + \text{In-migrants} – \text{Deaths} – \text{Out-migrants}$$Solving for Rate (R)
Growth: $\frac{R}{100} = \left(\frac{P_T}{P}\right)^{1/T} – 1$
Depreciation: $\frac{R}{100} = 1 – \left(\frac{P_T}{P}\right)^{1/T}$
Full Chapter PDF Manual
For offline study, access the complete PDF manual below.
Disclaimer
This pdf notes is based on old course but same as most of the question in new course and taken from manual written by:
- Title: Compulsory Maths SEE Manual
- Writer: Dr Simkhada
- Publisher: Readmore Publishers & Distributors
- Edition: 2076
Additional References
For further reading on the mathematics curriculum in Nepal including this chapter, please visit the Ministry of Education, Science and Technology.