Solving the Fridge and Washing Machine Cost Price Problem

This problem involves calculating the original cost price of a washing machine given the total cost of a fridge and washing machine, the profit/loss percentages on their sales, and the fact that they were sold at the same price.

Understanding the Given Information

• Total cost price of fridge and washing machine = Rs. 57300
• Fridge sold at a profit of 15%
• Washing machine sold at a loss of 24%
• Both were sold at the same selling price.

Setting up the Equations

Let the cost price of the fridge be \(C_F\) and the cost price of the washing machine be \(C_W\).

From the problem statement, we have the following relationship for the total cost price:

\(C_F + C_W = 57300 \quad (1)\)

Now, let's look at the selling prices. The selling price (SP) is calculated differently for profit and loss:

• Selling Price = Cost Price + Profit (for profit)
• Selling Price = Cost Price - Loss (for loss)

Profit/Loss is given as a percentage of the cost price.

• Profit on fridge = 15% of \(C_F\) = \(0.15 C_F\)
• Loss on washing machine = 24% of \(C_W\) = \(0.24 C_W\)

The selling price of the fridge (\(S_F\)) is:

\(S_F = C_F + 0.15 C_F = C_F (1 + 0.15) = 1.15 C_F\)

The selling price of the washing machine (\(S_W\)) is:

\(S_W = C_W - 0.24 C_W = C_W (1 - 0.24) = 0.76 C_W\)

The problem states that the selling prices are the same:

\(S_F = S_W\)

So, we have:

\(1.15 C_F = 0.76 C_W \quad (2)\)

Solving for the Cost Price of the Washing Machine (\(C_W\))

We now have a system of two linear equations with two variables (\(C_F\) and \(C_W\)):

1. \(C_F + C_W = 57300\)
2. \(1.15 C_F = 0.76 C_W\)

From equation (2), we can express \(C_F\) in terms of \(C_W\):

\(C_F = \frac{0.76}{1.15} C_W\)

To simplify the fraction, multiply the numerator and denominator by 100:

\(C_F = \frac{76}{115} C_W\)

Now, substitute this expression for \(C_F\) into equation (1):

\(\frac{76}{115} C_W + C_W = 57300\)

Combine the \(C_W\) terms:

\(\left(\frac{76}{115} + 1\right) C_W = 57300\)

\(\left(\frac{76 + 115}{115}\right) C_W = 57300\)

\(\left(\frac{191}{115}\right) C_W = 57300\)

Now, solve for \(C_W\):

\(C_W = 57300 \times \frac{115}{191}\)

Let's perform the division:

\(57300 \div 191\)

We can see that \(191 \times 3 = 573\). So, \(57300 \div 191 = 300\).

\(C_W = 300 \times 115\)

\(C_W = 34500\)

So, the cost price of the washing machine is Rs. 34500.

We can also find the cost price of the fridge to verify:

\(C_F = 57300 - C_W = 57300 - 34500 = 22800\)

Let's check the selling prices:

\(S_F = 1.15 \times C_F = 1.15 \times 22800 = 26220\)

\(S_W = 0.76 \times C_W = 0.76 \times 34500 = 26220\)

Since \(S_F = S_W = 26220\), our calculation is correct.

Final Answer

The cost price of the washing machine is Rs. 34500.

Revision Table: Profit and Loss Calculations

Additional Information: Concepts in Profit and Loss

Understanding the basic concepts of cost price, selling price, profit, and loss is crucial for solving such problems.

• Cost Price (CP): This is the original price at which an item is bought.
• Selling Price (SP): This is the price at which an item is sold.
• Profit: Occurs when SP > CP. Profit = SP - CP. Profit percentage is calculated on CP: Profit % = \(\frac{\text{Profit}}{CP} \times 100\).
• Loss: Occurs when SP < CP. Loss = CP - SP. Loss percentage is calculated on CP: Loss % = \(\frac{\text{Loss}}{CP} \times 100\).

In this problem, we used the direct relationship between CP and SP based on the percentage profit or loss. If an item is sold at a 15% profit, the selling price is 115% of the cost price (100% CP + 15% Profit). If an item is sold at a 24% loss, the selling price is 76% of the cost price (100% CP - 24% Loss). These relationships are represented by the factors 1.15 and 0.76 in our calculations.