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

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

### Step 2: Set Up Equations for June
From the problem, we know:
1. The total number of bottles sold in June is 1000:
\[ x + y = 1000 \quad \text{(Equation 1)} \]
2. The total sales amount to Rs. 10,820:
\[ 10x + 12y = 10820 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations for June
We can solve these two equations simultaneously.

From Equation 1:
\[ y = 1000 - x \]

Substituting \( y \) in Equation 2:
\[ 10x + 12(1000 - x) = 10820 \]
\[ 10x + 12000 - 12x = 10820 \]
\[ -2x + 12000 = 10820 \]
\[ -2x = 10820 - 12000 \]
\[ -2x = -1180 \]
\[ x = 590 \]

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

So, in June:
- Alpha sanitizer bottles sold: \( x = 590 \)
- Beta sanitizer bottles sold: \( y = 410 \)

### Step 4: Set Up Equations for July
In July, the price of both sanitizers increases by Rs. 1:
- Price of Alpha = Rs. 11
- Price of Beta = Rs. 13

The total number of bottles sold in July is 2500:
\[ x' + y' = 2500 \quad \text{(Equation 3)} \]
The total sales amount to Rs. 29,200:
\[ 11x' + 13y' = 29200 \quad \text{(Equation 4)} \]

### Step 5: Solve the Equations for July
From Equation 3:
\[ y' = 2500 - x' \]

Substituting \( y' \) in Equation 4:
\[ 11x' + 13(2500 - x') = 29200 \]
\[ 11x' + 32500 - 13x' = 29200 \]
\[ -2x' + 32500 = 29200 \]
\[ -2x' = 29200 - 32500 \]
\[ -2x' = -3300 \]
\[ x' = 1650 \]

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

So, in July:
- Alpha sanitizer bottles sold: \( x' = 1650 \)
- Beta sanitizer bottles sold: \( y' = 850 \)

### Step 6: Calculate the Percent Increase in Alpha Sanitizer
To find the percent increase:
\[ \text{Increase} = x' - x = 1650 - 590 = 1060 \]
\[ \text{Percent Increase} = \left( \frac{\text{Increase}}{x} \right) \times 100 = \left( \frac{1060}{590} \right) \times 100 \]
\[ \text{Percent Increase} \approx 179.66\% \]

### Final Answer
The percent increase in Alpha sanitizer in July as compared to June is approximately **179.66%**.

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