Raj and Vinay are participating in the "Tree Plantation Drive". Raj plants `30%` of the plants and then Vinay came and planned 117 plants. If `25%` of the plants are still to be planted, find the total number of plants that were to be planted.

Answer

To solve the problem step by step, we need to find the total number of plants that were to be planted, given that Raj planted 30% of the total plants, Vinay planted 117 plants, and 25% of the plants are still to be planted.

### Step 1: Define the total number of plants
Let the total number of plants to be planted be denoted as \( X \).

### Step 2: Calculate the percentage of plants already planted
Raj planted 30% of the total plants, which can be expressed as:
\[ \text{Plants planted by Raj} = \frac{30}{100} \times X = 0.3X \]
Vinay planted 117 plants.

### Step 3: Calculate the total number of plants planted so far
The total number of plants that have been planted by both Raj and Vinay is:
\[ \text{Total plants planted} = 0.3X + 117 \]

### Step 4: Determine the percentage of plants still to be planted
According to the problem, 25% of the plants are still to be planted. Therefore, the percentage of plants that have already been planted is:
\[ 100\% - 25\% = 75\% \]
This means that the total number of plants planted is 75% of \( X \):
\[ \text{Total plants planted} = \frac{75}{100} \times X = 0.75X \]

### Step 5: Set up the equation
Now, we can set up the equation based on the total plants planted:
\[ 0.3X + 117 = 0.75X \]

### Step 6: Solve for \( X \)
To solve for \( X \), we will rearrange the equation:
\[ 117 = 0.75X - 0.3X \]
\[ 117 = 0.45X \]

Now, divide both sides by 0.45 to find \( X \):
\[ X = \frac{117}{0.45} \]

### Step 7: Calculate \( X \)
Calculating \( \frac{117}{0.45} \):
\[ X = 117 \times \frac{100}{45} = 117 \times \frac{20}{9} = \frac{2340}{9} = 260 \]

### Conclusion
The total number of plants that were to be planted is \( \boxed{260} \).

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