A full-sleeve shirt costs Rs 75 more than a half-sleeve shirt. If the cost of 4 full-sleeve shirts and 5 halfsleeve shirts cost Rs2325, find the cost of each.

Answer

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

### Step 1: Define the Variables
Let the cost of a half-sleeve shirt be \( x \) (in Rs).
Then, the cost of a full-sleeve shirt would be \( x + 75 \) (since it costs Rs 75 more than the half-sleeve shirt).

### Step 2: Set Up the Equation
According to the problem, the total cost of 4 full-sleeve shirts and 5 half-sleeve shirts is Rs 2325.
We can express this as:
\[ 4 \times (x + 75) + 5 \times x = 2325 \]

### Step 3: Expand the Equation
Now, let's expand the equation:
\[ 4(x + 75) + 5x = 2325 \]
This simplifies to:
\[ 4x + 300 + 5x = 2325 \]

### Step 4: Combine Like Terms
Combine the terms involving \( x \):
\[ (4x + 5x) + 300 = 2325 \]
This gives us:
\[ 9x + 300 = 2325 \]

### Step 5: Isolate the Variable
Now, we need to isolate \( x \) by subtracting 300 from both sides:
\[ 9x = 2325 - 300 \]
This simplifies to:
\[ 9x = 2025 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 9 to find \( x \):
\[ x = \frac{2025}{9} \]
Calculating this gives:
\[ x = 225 \]

### Step 7: Find the Cost of Each Shirt
Now that we have \( x \), we can find the cost of each shirt:
- Cost of half-sleeve shirt = \( x = 225 \) Rs
- Cost of full-sleeve shirt = \( x + 75 = 225 + 75 = 300 \) Rs

### Final Answer
- Cost of half-sleeve shirt = Rs 225
- Cost of full-sleeve shirt = Rs 300

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