Two old cars are sold for Rs. 48,000 each. One is sold at a profit of 20% and another at a loss of 20%. Find the net profit/loss percentage and the total amount of profit/loss.
4% loss, Rs. 4,000 loss
To solve this problem, we need to find the net profit or loss percentage when two cars are sold at Rs. 48,000 each, with one being sold at a 20% profit and the other at a 20% loss.
Step 1: Calculate Cost Price (CP) of Each Car
Let's assume the cost price of the first car is \( C_1 \) and the second car is \( C_2 \).
Car 1:
The selling price (SP) of Car 1 is Rs. 48,000 with a profit of 20%.
Using the profit formula:
\(SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right)\)
Therefore,
\(48,000 = C_1 \times \left(1 + \frac{20}{100}\right)\)
\(48,000 = C_1 \times 1.2\)
\(C_1 = \frac{48,000}{1.2} = 40,000\)
Car 2:
The selling price (SP) of Car 2 is Rs. 48,000 with a loss of 20%.
Using the loss formula:
\(SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right)\)
Therefore,
\(48,000 = C_2 \times \left(1 - \frac{20}{100}\right)\)
\(48,000 = C_2 \times 0.8\)
\(C_2 = \frac{48,000}{0.8} = 60,000\)
Step 2: Calculate Total Cost Price and Total Selling Price
Total cost price (TCP) = \( C_1 + C_2 = 40,000 + 60,000 = 100,000 \)
Total selling price (TSP) = 48,000 + 48,000 = 96,000
Step 3: Calculate Net Loss and Loss Percentage
Net loss = TCP - TSP = 100,000 - 96,000 = Rs. 4,000
Net loss percentage = \(\left(\frac{\text{Net Loss}}{\text{TCP}}\right) \times 100 = \left(\frac{4,000}{100,000}\right) \times 100 = 4\%\)
Thus, the net result is a 4% loss, and the total amount of loss is Rs. 4,000.
Conclusion:
The correct answer is 4% loss, Rs. 4,000 loss.
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