Question

Calculate the number of plants in qunicunx system of planting in one hectare area when row to row and plant to plant distance is 10 m

• A. 90
• B. 150
• C. 181
• D. 200

Hint:

For a standard 1-hectare plot with $10\text{ m}$ spacing:
- Square system has exactly 100 plants ($10 \times 10$).
- Filler plants are always $(n-1)^2 = (10-1)^2 = 81$.
- Total quincunx plants = $100 + 81 = 181$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The quincunx (or filler) system of orchard planting is a modification of the square system.
In this system, plants are set at the corners of a square, and an additional temporary crop or "filler plant" is planted in the center of each square to optimize land-use efficiency during the early years of the orchard.
Key Formula or Approach:
For a square plot of area $L \times W$:
1. Number of main plants along the length:
\[ n_L = \frac{L}{S} \]
2. Number of main plants along the width:
\[ n_W = \frac{W}{S} \]
3. Total number of main plants in the square system ($N_s$):
\[ N_s = n_L \times n_W \]
4. Number of filler plants in the quincunx system ($N_f$):
\[ N_f = (n_L - 1) \times (n_W - 1) \]
5. Total plants in the quincunx system:
\[ N_q = N_s + N_f \]

Step 2: Detailed Explanation:
Let us perform the calculations for a 1-hectare square area ($100\text{ m} \times 100\text{ m}$) with a spacing ($S$) of $10\text{ m}$:
-
Step 1: Calculate the number of main plants along the length and width:
\[ n_L = \frac{100}{10} = 10 \]
\[ n_W = \frac{100}{10} = 10 \]
- Calculate the total number of main plants ($N_s$):
\[ N_s = 10 \times 10 = 100 \text{ plants} \]
-
Step 2: Calculate the number of filler plants ($N_f$):
\[ N_f = (10 - 1) \times (10 - 1) \]
\[ N_f = 9 \times 9 = 81 \text{ plants} \]
-
Step 3: Calculate the total number of plants in the quincunx system ($N_q$):
\[ N_q = N_s + N_f \]
\[ N_q = 100 + 81 = 181 \text{ plants} \]
This matches Option (C).

Step 3: Final Answer:
The number of plants in the quincunx system of planting is 181.