The cost price of a set of 2 pants + 4 shirts or 1 pant+ 6 shirts is Rs. 5,600. A shopkeeper decided to sell them separately. He sold 10 shirts for Rs 6,000. Find the amount of profit or loss per shirt.

Options

A. Profit Rs. 1000
B. Loss Rs 1000
C. Profit Rs. 100
D. Loss Rs 100

Answer

To solve the problem step by step, we need to determine the cost price of one shirt and then compare it with the selling price to find the profit or loss per shirt.

### Step 1: Understand the Cost Price of the Sets
We know that the cost price of a set of:
- 2 pants + 4 shirts = Rs. 5,600
- 1 pant + 6 shirts = Rs. 5,600

Let’s denote:
- Cost price of 1 pant = P
- Cost price of 1 shirt = S

From the first set, we can write the equation:
\[ 2P + 4S = 5600 \] (Equation 1)

From the second set, we can write:
\[ P + 6S = 5600 \] (Equation 2)

### Step 2: Solve the Equations
We can solve these two equations to find the values of P and S.

From Equation 2, we can express P in terms of S:
\[ P = 5600 - 6S \] (Equation 3)

Now, substitute Equation 3 into Equation 1:
\[ 2(5600 - 6S) + 4S = 5600 \]
\[ 11200 - 12S + 4S = 5600 \]
\[ 11200 - 8S = 5600 \]
\[ -8S = 5600 - 11200 \]
\[ -8S = -5600 \]
\[ S = \frac{5600}{8} = 700 \]

Now that we have the cost price of one shirt, we can find P using Equation 3:
\[ P = 5600 - 6(700) \]
\[ P = 5600 - 4200 = 1400 \]

### Step 3: Selling Price of the Shirts
The shopkeeper sold 10 shirts for Rs. 6,000. Therefore, the selling price (SP) of one shirt is:
\[ SP = \frac{6000}{10} = 600 \]

### Step 4: Calculate Profit or Loss
Now we can calculate the profit or loss per shirt:
- Cost Price (CP) of one shirt = Rs. 700
- Selling Price (SP) of one shirt = Rs. 600

Now, we find the loss:
\[ \text{Loss} = CP - SP = 700 - 600 = 100 \]

### Conclusion
The shopkeeper incurs a loss of Rs. 100 per shirt.