Cost Price Calculation for Frocks

This solution details the steps to calculate the cost price of the first frock, given the total purchase price, individual selling conditions (loss percentage for the first frock and gain percentage for the second), and the overall break-even outcome.

Information Summary

• Total Cost Price (CP_Total): ₹1,200
• Frock 1: Sold at a 7% loss. Its cost price is CP₁.
• Frock 2: Sold at a 23% gain. Its cost price is CP₂.
• Overall Result: No profit, no loss. This implies Total Selling Price (SP_Total) = CP_Total.

Formulating Equations

Based on the information provided, we can establish the following relationships:

1. Sum of individual cost prices: CP₁ + CP₂ = ₹1,200
2. Selling Price of Frock 1 (SP₁): SP₁ = CP₁ × (1 - 7/100) = CP₁ × 0.93
3. Selling Price of Frock 2 (SP₂): SP₂ = CP₂ × (1 + 23/100) = CP₂ × 1.23
4. Total Selling Price equals Total Cost Price: SP₁ + SP₂ = ₹1,200

Solving for CP₁

Substitute the expressions for SP₁ and SP₂ into the total selling price equation:

$ ( \text{CP}_{1} \times 0.93 ) + ( \text{CP}_{2} \times 1.23 ) = 1200 $

Use the relationship CP₂ = 1200 - CP₁ from the first equation and substitute it:

$ ( \text{CP}_{1} \times 0.93 ) + ( (1200 - \text{CP}_{1}) \times 1.23 ) = 1200 $

Expand and rearrange the equation to solve for CP₁:

$ 0.93 \times \text{CP}_{1} + 1476 - 1.23 \times \text{CP}_{1} = 1200 $

Combine terms involving CP₁:

$ (0.93 - 1.23) \times \text{CP}_{1} = 1200 - 1476 $

$ -0.30 \times \text{CP}_{1} = -276 $

Calculate the value of CP₁:

$ \text{CP}_{1} = \frac{-276}{-0.30} = \frac{276}{0.30} $

$ \text{CP}_{1} = 920 $

Conclusion

The cost price (in ₹) of the first frock is 920.