In 1998, ratio of the numbers of students taking examinations in x and z states are respectively 3:5:6. Next year, the numbers of students are increased by 20%, 10% and 20% respectively. If ratio of the numbers of students in states x and z is 1 : 2, then find the number of students who sit to take examination in 1998.

Options

A. 5000
B. 6000
C. 75000
D. Data is insufficient

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the number of students in each state in 1998
Let the number of students in states X, Y, and Z in 1998 be represented as:
- Students in state X = 3x
- Students in state Y = 5x
- Students in state Z = 6x

### Step 2: Calculate the number of students after the increase
Next, we will calculate the number of students in each state after the given percentage increases:
- For state X (20% increase):
\[ \text{New students in X} = 3x \times 1.2 = 3.6x \]

- For state Y (10% increase):
\[ \text{New students in Y} = 5x \times 1.1 = 5.5x \]

- For state Z (20% increase):
\[ \text{New students in Z} = 6x \times 1.2 = 7.2x \]

### Step 3: Set up the ratio of students in states X and Z
According to the problem, the ratio of the number of students in states X and Z after the increase is given as 1:2. Therefore, we can set up the equation:
\[ \frac{3.6x}{7.2x} = \frac{1}{2} \]

### Step 4: Simplify the ratio
We can simplify the left side of the equation:
\[ \frac{3.6}{7.2} = \frac{1}{2} \]

This simplifies to:
\[ \frac{1}{2} = \frac{1}{2} \]

### Step 5: Conclusion
Since the equation holds true, we can conclude that the values of x are consistent with the given ratio. However, we need to find the actual number of students in 1998.

### Step 6: Find the total number of students
To find the total number of students in 1998, we can express it as:
\[ \text{Total students} = 3x + 5x + 6x = 14x \]

### Step 7: Determine the value of x
Since we do not have a specific value for x, we cannot determine the exact number of students. Therefore, we conclude that the information provided is insufficient to find the total number of students.

### Final Answer
The answer is that the data is insufficient to determine the exact number of students who sat for the examination in 1998.

---