Radha bought a fridge and a washing machine together for Rs. 57300. She sold the fridge at a profit of 15% and washing machine at a loss of 24% and both are sold at the same price. The cost price of washing machine (in Rs.) is:
34500
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 \(C_W\)):
- \(C_F + C_W = 57300\)
- \(1.15 C_F = 0.76 C_W\)
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
| Concept | Formula (as a decimal) | Formula (as a fraction) |
|---|---|---|
| Selling Price (with Profit) | \(SP = CP \times (1 + \text{Profit %})\) | \(SP = CP \times \left(1 + \frac{\text{Profit %}}{100}\right)\) |
| Selling Price (with Loss) | \(SP = CP \times (1 - \text{Loss %})\) | \(SP = CP \times \left(1 - \frac{\text{Loss %}}{100}\right)\) |
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.
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