5 bottles cost as much as 2 bags. The cost of 15 bottles and 4 bags in Rs 2,000. What is the price (in Rs.) of a single bag ?

Options

A. 200
B. 215
C. 240
D. 250

Answer

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

### Step 1: Define Variables
Let the price of one bag be \( X \) (in Rs).

### Step 2: Establish Relationship Between Bottles and Bags
According to the problem, the cost of 5 bottles is equal to the cost of 2 bags. Therefore, we can express the cost of 5 bottles in terms of \( X \):
\[ 5B = 2X \]
Where \( B \) is the price of one bottle.

### Step 3: Express the Cost of Bottles
From the equation above, we can express the cost of one bottle \( B \) in terms of \( X \):
\[ B = \frac{2X}{5} \]

### Step 4: Set Up the Total Cost Equation
We are also given that the total cost of 15 bottles and 4 bags is Rs 2000. We can express this as:
\[ 15B + 4X = 2000 \]

### Step 5: Substitute the Value of B
Now, substitute the value of \( B \) from Step 3 into the total cost equation:
\[ 15\left(\frac{2X}{5}\right) + 4X = 2000 \]

### Step 6: Simplify the Equation
Now simplify the equation:
\[ 3(2X) + 4X = 2000 \]
\[ 6X + 4X = 2000 \]
\[ 10X = 2000 \]

### Step 7: Solve for X
Now, divide both sides by 10 to find \( X \):
\[ X = \frac{2000}{10} = 200 \]

### Step 8: Conclusion
The price of one bag is Rs 200.