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The problem asks to write up the Plant and Machinery Account for the four years ending on 31st December 2022, including the calculation of depreciation using the diminishing balance method at 10% per annum.

Here is the information extracted from the image:

1. **Initial Value (on 1st January 2019):** ₹1,00,000
2. **New Machine Purchase (on 15th July 2020):**
   - Cost of the machine: ₹40,000
   - Installation charges: ₹5,000
   - Total cost: ₹45,000
3. **Sale of the new machine (on 1st September 2022):**
   - Sold for a profit of ₹7,000
4. **Depreciation:** 10% p.a. under the diminishing balance method.

### Steps to Solve:

1. **Depreciation for the year 2019:**
   Depreciation on ₹1,00,000 at 10% p.a.
   \[
   \text{Depreciation} = 1,00,000 \times 0.10 = ₹10,000
   \]
   Closing balance for 2019:
   \[
   1,00,000 - 10,000 = ₹90,000
   \]

2. **Depreciation for the year 2020:**
   The machine worth ₹45,000 was purchased mid-year, so the depreciation will be calculated separately for this machine from 15th July 2020.
   
   - Depreciation for the original machine (₹90,000) at 10%:
     \[
     \text{Depreciation} = 90,000 \times 0.10 = ₹9,000
     \]
   - Depreciation for the new machine (₹45,000) from 15th July 2020 (half-year depreciation):
     \[
     \text{Depreciation} = 45,000 \times 0.10 \times \frac{6}{12} = ₹2,250
     \]
   
   Total depreciation for 2020:
   \[
   ₹9,000 + ₹2,250 = ₹11,250
   \]

   Closing balance for 2020:
   - For the original machine: ₹90,000 - ₹9,000 = ₹81,000
   - For the new machine: ₹45,000 - ₹2,250 = ₹42,750
   Total closing balance = ₹81,000 + ₹42,750 = ₹1,23,750

3. **Depreciation for the year 2021:**
   - Depreciation on ₹81,000 (old machine):
     \[
     \text{Depreciation} = 81,000 \times 0.10 = ₹8,100
     \]
   - Depreciation on ₹42,750 (new machine):
     \[
     \text{Depreciation} = 42,750 \times 0.10 = ₹4,275
     \]
   
   Total depreciation for 2021:
   \[
   ₹8,100 + ₹4,275 = ₹12,375
   \]
   
   Closing balance for 2021:
   - Old machine: ₹81,000 - ₹8,100 = ₹72,900
   - New machine: ₹42,750 - ₹4,275 = ₹38,475
   Total closing balance = ₹72,900 + ₹38,475 = ₹1,11,375

4. **Depreciation for 2022 (until sale of new machine):**
   - Depreciation on the old machine (₹72,900) up to 31st December:
     \[
     \text{Depreciation} = 72,900 \times 0.10 = ₹7,290
     \]
   - Depreciation on the new machine (₹38,475) until the sale on 1st September (8 months depreciation):
     \[
     \text{Depreciation} = 38,475 \times 0.10 \times \frac{8}{12} = ₹2,565
     \]
   
   Total depreciation up to 1st September:
   \[
   ₹7,290 + ₹2,565 = ₹9,855
   \]

5. **Sale of the machine on 1st September 2022:**
   The new machine (₹38,475 book value) is sold at a profit of ₹7,000. Therefore, the sale price is:
   \[
   \text{Sale Price} = 38,475 + 7,000 = ₹45,475
   \]

---

With these calculations, you can now create the Plant and Machinery account for the four years.

Would you like me to format the full account table for better clarity? Let me know if you need any additional details or explanation!

Here are 5 related questions for further understanding:

1. How does the diminishing balance method differ from straight-line depreciation?
2. What would be the book value of the machine if it was not sold in 2022?
3. How do installation charges affect the cost of an asset in accounting?
4. How would the calculations change if the machine was sold at a loss instead of a profit?
5. Can you explain how partial-year depreciation is calculated?

**Tip:** When selling an asset, always ensure to adjust for accumulated depreciation before determining profit or loss from the sale.

Plant and machinery having value of ₹1,00,000 was bought on 1st January, 2019. On 15th July, 2020, a new machine was purchased for ₹40,000. Installation charges paid for this machine was ₹5,000. The machine (bought on 15th July, 2020) was sold at a profit of ₹7,000 on 1st September, 2022. Write up the plant and machinery account for the four years ended 31st December, 2022 providing 10% p.a. depreciation under the diminishing balance method.

This problem calculates the plant and machinery account for a four-year period ending in 2022. It covers depreciation using the diminishing balance method at 10% per annum and accounts for partial-year depreciation and the sale of a machine. Suitable for undergraduate-level students studying accounting or finance.

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