A box contain 3600 balls of red, blue, green, and black colours in the ratio `3:4:5:6` . Find the number and percentage of balls of each off the four colours in the box.

Answer

To solve the problem step by step, we will first determine the number of balls of each color based on the given ratio and then calculate the percentage of each color.

### Step 1: Understand the Ratio
The ratio of red, blue, green, and black balls is given as 3:4:5:6. This means:
- Red balls = 3 parts
- Blue balls = 4 parts
- Green balls = 5 parts
- Black balls = 6 parts

### Step 2: Calculate the Total Parts
To find the total number of parts in the ratio, we add all the parts together:
\[ \text{Total parts} = 3 + 4 + 5 + 6 = 18 \]

### Step 3: Calculate the Value of Each Part
The total number of balls is 3600. To find the value of one part, we divide the total number of balls by the total parts:
\[ \text{Value of one part} = \frac{3600}{18} = 200 \]

### Step 4: Calculate the Number of Balls of Each Color
Now we can find the number of balls for each color by multiplying the number of parts for each color by the value of one part.

- **Red Balls**:
\[ \text{Number of Red Balls} = 3 \times 200 = 600 \]

- **Blue Balls**:
\[ \text{Number of Blue Balls} = 4 \times 200 = 800 \]

- **Green Balls**:
\[ \text{Number of Green Balls} = 5 \times 200 = 1000 \]

- **Black Balls**:
\[ \text{Number of Black Balls} = 6 \times 200 = 1200 \]

### Step 5: Verify the Total Number of Balls
To ensure our calculations are correct, we can add the number of balls of each color:
\[ 600 + 800 + 1000 + 1200 = 3600 \]
This matches the total number of balls given in the problem.

### Step 6: Calculate the Percentage of Each Color
To find the percentage of each color, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Number of Balls of Color}}{\text{Total Number of Balls}} \right) \times 100 \]

- **Percentage of Red Balls**:
\[ \text{Percentage of Red} = \left( \frac{600}{3600} \right) \times 100 = 16.67\% \]

- **Percentage of Blue Balls**:
\[ \text{Percentage of Blue} = \left( \frac{800}{3600} \right) \times 100 = 22.22\% \]

- **Percentage of Green Balls**:
\[ \text{Percentage of Green} = \left( \frac{1000}{3600} \right) \times 100 = 27.78\% \]

- **Percentage of Black Balls**:
\[ \text{Percentage of Black} = \left( \frac{1200}{3600} \right) \times 100 = 33.33\% \]

### Final Results
- Number of Red Balls: 600 (16.67%)
- Number of Blue Balls: 800 (22.22%)
- Number of Green Balls: 1000 (27.78%)
- Number of Black Balls: 1200 (33.33%)