Calculating Effective Profit/Loss Percentage
Let the cost price (CP) of the first article be CP1 and the selling price (SP) be SP1. Let the cost price of the second article be CP2 and the selling price be SP2.
Step 1: Calculate SP1 and CP2
The first article is sold at a 20% profit. If we assume CP1 = $100 (for simplicity):
SP1 = CP1 * (1 + Profit%)
SP1 = $100 * (1 + \frac{20}{100}) = $100 * 1.20 = $120
We are given that the selling price of the first article equals the cost price of the second article:
SP1 = CP2
Therefore, CP2 = $120.
Step 2: Calculate SP2
The second article is sold at a 20% loss:
SP2 = CP2 * (1 - Loss%)
SP2 = $120 * (1 - \frac{20}{100}) = $120 * 0.80 = $96
Step 3: Calculate Total CP and Total SP
Total Cost Price (Total CP) = CP1 + CP2 = $100 + $120 = $220
Total Selling Price (Total SP) = SP1 + SP2 = $120 + $96 = $216
Step 4: Determine Effective Profit/Loss Percentage
Since Total SP ($216) is less than Total CP ($220), there is an overall loss.
Loss = Total CP - Total SP = $220 - $216 = $4
Effective Loss Percentage = (Loss / Total CP) * 100
Effective Loss Percentage = \(\frac{4}{220} \times 100\)
Effective Loss Percentage = \(\frac{400}{220}\) = \(\frac{20}{11}\) %
Effective Loss Percentage ≈ 1.818...%
Approximately, the effective loss is 1.8%.
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Important Questions from Profit and Loss
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An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
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If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
An article when sold at a gain of 5%, yields Rs. 15 more than when sold at a loss of 5%. The cost price will be
