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:
What percent of increase was found in alpha sanitizer in July as compared to June?

Options

A. `182%`
B. `79%`
C. `179.66%`
D. `50%`

Answer

To find the percentage increase in sales of Alpha sanitizer from June to July, we will follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = number of Alpha sanitizers sold in June
- \( y \) = number of Beta sanitizers sold in June

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of bottles sold in June:
\[ x + y = 1000 \quad \text{(Equation 1)} \]
2. The total sales amount in June:
\[ 10x + 12y = 10820 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 1000 - x \]

Substituting \( y \) into Equation 2:
\[ 10x + 12(1000 - x) = 10820 \]
Expanding this:
\[ 10x + 12000 - 12x = 10820 \]
Combining like terms:
\[ -2x + 12000 = 10820 \]
Rearranging gives:
\[ -2x = 10820 - 12000 \]
\[ -2x = -1180 \]
Dividing by -2:
\[ x = 590 \]

Now substituting \( x \) back to find \( y \):
\[ y = 1000 - 590 = 410 \]

### Step 4: Calculate Sales in July
In July, the prices of the sanitizers increased by Rs. 1:
- Price of Alpha = Rs. 11
- Price of Beta = Rs. 13

Let:
- \( a \) = number of Alpha sanitizers sold in July
- \( b \) = number of Beta sanitizers sold in July

We know:
1. The total number of bottles sold in July:
\[ a + b = 2500 \quad \text{(Equation 3)} \]
2. The total sales amount in July:
\[ 11a + 13b = 29200 \quad \text{(Equation 4)} \]

### Step 5: Solve for \( a \) and \( b \)
From Equation 3, express \( b \):
\[ b = 2500 - a \]

Substituting into Equation 4:
\[ 11a + 13(2500 - a) = 29200 \]
Expanding:
\[ 11a + 32500 - 13a = 29200 \]
Combining like terms:
\[ -2a + 32500 = 29200 \]
Rearranging gives:
\[ -2a = 29200 - 32500 \]
\[ -2a = -3300 \]
Dividing by -2:
\[ a = 1650 \]

Now substituting back to find \( b \):
\[ b = 2500 - 1650 = 850 \]

### Step 6: Calculate Percentage Increase
Now we have:
- Sales of Alpha in June = 590
- Sales of Alpha in July = 1650

To find the percentage increase:
\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{1650 - 590}{590} \right) \times 100 \]
Calculating:
\[ \text{Percentage Increase} = \left( \frac{1060}{590} \right) \times 100 \approx 179.66\% \]

### Final Answer
The percentage increase in sales of Alpha sanitizer in July compared to June is approximately **179.66%**.