Case Study-2: A company manufactores two types of sanitizers Alpha and Beta. The cost of the small bottle of Alpha sanitizer is Rs. 10 and for beta sanitizer is Rs. 12. In the month of June, the company sold total 1000 bottles and makes a total sale of Rs. 10,820. Seeing the great demand and short of supply, company decided to increase the price of both the sanitizer by Rs. 1. In the next month i.e. July, the company sold 2,500 bottles and total sales of Rs. 29,200.
Answer the following questions:
How many bottles of each type were sold in the next month when rate was increased?

Options

A. 1200, 1300
B. 1300, 1200
C. 1550, 950
D. 1650, 850

Answer

To solve the problem, we need to set up equations based on the information provided. Let's denote:
- \( x \) = number of bottles of Alpha sanitizer sold in July
- \( y \) = number of bottles of Beta sanitizer sold in July

### Step 1: Set up the equations based on the total bottles sold
From the information given, we know that the total number of bottles sold in July is 2,500. Therefore, we can write the first equation as:
\[ x + y = 2500 \quad \text{(1)} \]

### Step 2: Set up the equation based on total sales
Next, we need to consider the prices after the increase. The price of Alpha sanitizer in July is Rs. 11 and the price of Beta sanitizer is Rs. 13. The total sales amount to Rs. 29,200. Thus, we can write the second equation as:
\[ 11x + 13y = 29200 \quad \text{(2)} \]

### Step 3: Solve the equations
Now, we can solve these two equations simultaneously. We will use equation (1) to express \( y \) in terms of \( x \):
\[ y = 2500 - x \quad \text{(3)} \]

Now, substitute equation (3) into equation (2):
\[ 11x + 13(2500 - x) = 29200 \]
Expanding this gives:
\[ 11x + 32500 - 13x = 29200 \]
Combining like terms:
\[ -2x + 32500 = 29200 \]
Now, isolate \( x \):
\[ -2x = 29200 - 32500 \]
\[ -2x = -3300 \]
\[ x = \frac{3300}{2} = 1650 \]

### Step 4: Find \( y \)
Now that we have \( x \), we can find \( y \) using equation (3):
\[ y = 2500 - 1650 = 850 \]

### Conclusion
Thus, the number of bottles sold in July is:
- Alpha sanitizer: 1650 bottles
- Beta sanitizer: 850 bottles