A confectionery sells two types of chocolate boxes, medium and small. The medium box costs Rs 50 more than the small box. The cost of three medium boxes and four small boxes is Rs 1550. Find the cost of each.

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( x \) = cost of the small box
- \( y \) = cost of the medium box

### Step 2: Set Up the Equations
From the problem, we know:
1. The medium box costs Rs 50 more than the small box:
\[ y = x + 50 \quad \text{(Equation 1)} \]

2. The total cost of three medium boxes and four small boxes is Rs 1550:
\[ 3y + 4x = 1550 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 1 into Equation 2
Now, we will substitute the value of \( y \) from Equation 1 into Equation 2:
\[ 3(x + 50) + 4x = 1550 \]

### Step 4: Simplify the Equation
Distributing the 3 in the equation:
\[ 3x + 150 + 4x = 1550 \]
Combine like terms:
\[ 7x + 150 = 1550 \]

### Step 5: Solve for \( x \)
Now, subtract 150 from both sides:
\[ 7x = 1550 - 150 \]
\[ 7x = 1400 \]
Now, divide both sides by 7:
\[ x = \frac{1400}{7} \]
\[ x = 200 \]

### Step 6: Find the Cost of the Medium Box
Now that we have \( x \), we can find \( y \):
\[ y = x + 50 = 200 + 50 = 250 \]

### Final Answer
The cost of the small box is Rs 200, and the cost of the medium box is Rs 250.

### Summary of the Solution
- Cost of small box \( (x) = Rs 200 \)
- Cost of medium box \( (y) = Rs 250 \)