A contractor deployed some men to plant 1800 trees in a certain no. of days but in `1/3` rd of the planned time 120 plants could be planted so to full fill the target for the rest of the days every day 20 more plants were planted. Thus it saved on day out of the initially planned no. of days. How many plants he planned to plant each day initially?

Options

A. a. 180
B. b. 100
C. c. 120
D. d. 160

Answer

To solve the problem step by step, we will break down the information given and calculate accordingly.

### Step 1: Understand the total work and initial plan
The contractor needs to plant a total of 1800 trees in a certain number of days. Let's denote the total number of days planned as \( D \).

### Step 2: Calculate the initial planting rate
If the contractor planned to plant 1800 trees in \( D \) days, the initial number of trees to be planted each day would be:
\[ \text{Initial daily planting rate} = \frac{1800}{D} \]

### Step 3: Analyze the progress in the first third of the time
According to the problem, in \( \frac{1}{3} \) of the planned time, only 120 trees were planted. This means:
\[ \text{Days worked} = \frac{D}{3} \]
In this time, the number of trees planted is 120.

### Step 4: Calculate the remaining trees and time
The remaining trees to be planted after the first third of the time is:
\[ \text{Remaining trees} = 1800 - 120 = 1680 \]
The remaining time after \( \frac{1}{3} \) of the planned time is:
\[ \text{Remaining days} = D - \frac{D}{3} = \frac{2D}{3} \]

### Step 5: Determine the new daily planting rate
To fulfill the target, the contractor decided to plant 20 more trees each day than initially planned. Therefore, the new daily planting rate becomes:
\[ \text{New daily planting rate} = \frac{1800}{D} + 20 \]

### Step 6: Set up the equation for the remaining work
The total number of trees that need to be planted in the remaining days is 1680. Thus, we can set up the equation:
\[ \left( \frac{1800}{D} + 20 \right) \cdot \frac{2D}{3} = 1680 \]

### Step 7: Solve for \( D \)
Expanding the equation:
\[ \frac{1800 \cdot 2D}{3D} + 20 \cdot \frac{2D}{3} = 1680 \]
This simplifies to:
\[ 1200 + \frac{40D}{3} = 1680 \]
Subtracting 1200 from both sides:
\[ \frac{40D}{3} = 480 \]
Multiplying both sides by 3:
\[ 40D = 1440 \]
Dividing by 40:
\[ D = 36 \]

### Step 8: Calculate the initial daily planting rate
Now that we have \( D \), we can find the initial daily planting rate:
\[ \text{Initial daily planting rate} = \frac{1800}{36} = 50 \]

### Step 9: Verify the solution
The contractor initially planned to plant 50 trees per day. In the first \( \frac{1}{3} \) of the time (12 days), he should have planted:
\[ 50 \times 12 = 600 \text{ trees} \]
However, only 120 trees were planted, leaving 1680 trees to be planted in the remaining 24 days.

With the new rate of 70 trees per day (50 + 20), the total trees planted in 24 days would be:
\[ 70 \times 24 = 1680 \text{ trees} \]
This confirms that the calculations are correct.

### Conclusion
The initial number of plants the contractor planned to plant each day is **50**.