There are two branches X and Y of a company ABC. There were, a total of 4500 employees in the company during 2011, In the year 2012. the number of employees in branch X was increased by 20% and that in branch Y by 15%. In 2012, total number of employees was 5300. How many employees were there in branch Y in the year

Options

A. 1700
B. 1700
C. 1800
D. 2000

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the Variables
Let:
- \( x \) = Number of employees in branch X in 2011
- \( y \) = Number of employees in branch Y in 2011

### Step 2: Set Up the First Equation
From the problem, we know that the total number of employees in 2011 was 4500. Therefore, we can write the first equation:
\[ x + y = 4500 \quad \text{(1)} \]

### Step 3: Calculate the Number of Employees in 2012
In 2012, the number of employees in branch X increased by 20%, and in branch Y, it increased by 15%. Thus, the number of employees in each branch in 2012 can be expressed as:
- Employees in branch X in 2012: \( x + 0.2x = 1.2x \)
- Employees in branch Y in 2012: \( y + 0.15y = 1.15y \)

### Step 4: Set Up the Second Equation
The total number of employees in 2012 was 5300. Therefore, we can write the second equation:
\[ 1.2x + 1.15y = 5300 \quad \text{(2)} \]

### Step 5: Solve the Equations
Now we have a system of equations:
1. \( x + y = 4500 \)
2. \( 1.2x + 1.15y = 5300 \)

From equation (1), we can express \( x \) in terms of \( y \):
\[ x = 4500 - y \quad \text{(3)} \]

### Step 6: Substitute Equation (3) into Equation (2)
Substituting \( x \) from equation (3) into equation (2):
\[ 1.2(4500 - y) + 1.15y = 5300 \]
Expanding this gives:
\[ 5400 - 1.2y + 1.15y = 5300 \]
Combining like terms:
\[ 5400 - 0.05y = 5300 \]

### Step 7: Isolate \( y \)
Now, isolate \( y \):
\[ 5400 - 5300 = 0.05y \]
\[ 100 = 0.05y \]
\[ y = \frac{100}{0.05} = 2000 \]

### Step 8: Find \( x \)
Now substitute \( y \) back into equation (3) to find \( x \):
\[ x = 4500 - 2000 = 2500 \]

### Conclusion
Thus, the number of employees in branch Y in the year 2011 was:
\[ \boxed{2000} \]