The cost of 2 sarees and 4 shirt is rs 16000 while 1 saree and 6 shirts cost the same. The cost of 12 shirts is

Options

A. 12000
B. 24000
C. 48000
D. Cannot be determined

Answer

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

### Step 1: Define the Variables
Let:
- \( x \) = cost of one saree
- \( y \) = cost of one shirt

### Step 2: Set Up the Equations
From the problem statement, we can derive the following equations:
1. The cost of 2 sarees and 4 shirts is Rs 16,000:
\[ 2x + 4y = 16000 \quad \text{(Equation 1)} \]
2. The cost of 1 saree and 6 shirts is also Rs 16,000:
\[ x + 6y = 16000 \quad \text{(Equation 2)} \]

### Step 3: Multiply Equation 2
To eliminate \( x \), we can multiply Equation 2 by 2:
\[ 2(x + 6y) = 2 \times 16000 \]
This gives us:
\[ 2x + 12y = 32000 \quad \text{(Equation 3)} \]

### Step 4: Subtract Equation 1 from Equation 3
Now we will subtract Equation 1 from Equation 3:
\[ (2x + 12y) - (2x + 4y) = 32000 - 16000 \]
This simplifies to:
\[ 12y - 4y = 16000 \]
\[ 8y = 16000 \]

### Step 5: Solve for \( y \)
Now, divide both sides by 8 to find \( y \):
\[ y = \frac{16000}{8} = 2000 \]

### Step 6: Find the Cost of 12 Shirts
Now that we have the cost of one shirt, we can find the cost of 12 shirts:
\[ \text{Cost of 12 shirts} = 12y = 12 \times 2000 = 24000 \]

### Final Answer
The cost of 12 shirts is Rs 24,000.

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