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 sanitizers of each type was sold in June?
A
460, 510
B
540, 460
C
410, 590
D
590, 410
Text Solution
AI Generated Solution
The correct Answer is:
To find out how many bottles of each type of sanitizer (Alpha and Beta) were sold in June, we can set up a system of equations based on the information provided.
### Step-by-Step Solution:
1. **Define Variables:**
Let:
- \( X \) = number of Alpha sanitizers sold
- \( Y \) = number of Beta sanitizers sold
2. **Set Up the Equations:**
From the problem, we have two key pieces of information:
- The total number of bottles sold in June is 1000.
- The total sales amount in June is Rs. 10,820.
This gives us the following equations:
\[
X + Y = 1000 \quad \text{(1)}
\]
\[
10X + 12Y = 10820 \quad \text{(2)}
\]
3. **Solve the First Equation for One Variable:**
From equation (1), we can express \( Y \) in terms of \( X \):
\[
Y = 1000 - X \quad \text{(3)}
\]
4. **Substitute into the Second Equation:**
Substitute equation (3) into equation (2):
\[
10X + 12(1000 - X) = 10820
\]
Simplifying this:
\[
10X + 12000 - 12X = 10820
\]
\[
-2X + 12000 = 10820
\]
5. **Isolate \( X \):**
Rearranging gives:
\[
-2X = 10820 - 12000
\]
\[
-2X = -1180
\]
Dividing both sides by -2:
\[
X = 590
\]
6. **Find \( Y \) Using Equation (3):**
Now substitute \( X \) back into equation (3) to find \( Y \):
\[
Y = 1000 - 590
\]
\[
Y = 410
\]
7. **Conclusion:**
Therefore, the number of sanitizers sold in June is:
- Alpha sanitizers (X) = 590
- Beta sanitizers (Y) = 410
### Final Answer:
- **Alpha sanitizers sold:** 590
- **Beta sanitizers sold:** 410
