The cost of pizza is `2(1)/(2)` times the cost of a burger. If the sum of cost of one burger a and one pizza is Rs. 105, then find the cost of the burger.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the cost of the burger be \( x \) (in Rs).

### Step 2: Express the Cost of Pizza
According to the problem, the cost of pizza is \( 2\frac{1}{2} \) times the cost of the burger. We can convert \( 2\frac{1}{2} \) into an improper fraction:
\[ 2\frac{1}{2} = \frac{5}{2} \]
Thus, the cost of pizza can be expressed as:
\[ \text{Cost of Pizza} = \frac{5}{2}x \]

### Step 3: Set Up the Equation
The problem states that the sum of the cost of one burger and one pizza is Rs. 105. Therefore, we can set up the following equation:
\[ x + \frac{5}{2}x = 105 \]

### Step 4: Combine Like Terms
To combine the terms on the left side of the equation, we can express \( x \) as \( \frac{2}{2}x \):
\[ \frac{2}{2}x + \frac{5}{2}x = 105 \]
This simplifies to:
\[ \frac{7}{2}x = 105 \]

### Step 5: Solve for \( x \)
To isolate \( x \), we can multiply both sides of the equation by \( \frac{2}{7} \):
\[ x = 105 \times \frac{2}{7} \]
Calculating the right side:
\[ x = 105 \div 7 \times 2 = 15 \times 2 = 30 \]

### Step 6: Conclusion
Thus, the cost of the burger is:
\[ \text{Cost of Burger} = Rs. 30 \]

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