To find the overall profit percentage 'x', we need to calculate the total selling price (SP) relative to the total cost price (CP) of the goods.
Assume Total Cost Price
Let the total cost price (CP) of all the goods be $100$. This assumption simplifies percentage calculations.
Calculate Batch 1 Details
Goods Percentage: 35%
CP of Batch 1: $35\%$ of $100 = 35$
Profit: 22%
SP of Batch 1: $35 \times (1 + \frac{22}{100}) = 35 \times 1.22 = 42.70$
Calculate Batch 2 Details
Remaining Goods after Batch 1: $100\% - 35\% = 65\%$
Goods Percentage for Batch 2: $40\%$ of $65\% = 0.40 \times 65\% = 26\%$
CP of Batch 2: $26\%$ of $100 = 26$
Profit: 37%
SP of Batch 2: $26 \times (1 + \frac{37}{100}) = 26 \times 1.37 = 35.62$
Calculate Batch 3 Details
Remaining Goods after Batch 2: $100\% - 35\% - 26\% = 39\%$
CP of Batch 3: $39\%$ of $100 = 39$
Loss: 38%
SP of Batch 3: $39 \times (1 - \frac{38}{100}) = 39 \times 0.62 = 24.18$
Determine Overall Profit
Total CP: $100$
Total SP: SP Batch 1 + SP Batch 2 + SP Batch 3
Total SP: $42.70 + 35.62 + 24.18 = 102.50$
Total Profit: Total SP - Total CP = $102.50 - 100 = 2.50$
Calculate Overall Profit Percentage (x)
The overall profit percentage 'x' is calculated as:
$ x = \frac{\text{Total Profit}}{\text{Total CP}} \times 100 $ $ x = \frac{2.50}{100} \times 100 $ $ x = 2.5\% $Therefore, the overall profit percentage is 2.5%.
Important Questions from Successive Selling
- A dealer buys two articles X and Y for ₹1,000 each. He marks each of them at the same price. He sells X by giving two successive discounts of 15% and 30% and still earns ₹337 as profit. If he sells Y at a single discount of 49%, then what is the profit percentage on Y?
- Find the single equivalent discount (rounded off to two decimal places) for successive discounts of 18%, 6% and 25%.
A shopkeeper marks the price of three identical articles, first, 60% above the Cost Price; second, 45% above the Cost Price and the third, 40% above the cost price. If he gives discount of 25% on first article, 20% on the second article and 15% on the third one, what is his overall profit percentage?
A dealer bought a six-seater Dining Table after getting successive discounts of 15% and 12%. Thereafter, he spent 10% on transport, etc. and finally sold it for Rs. 24,169.75, thereby earning a profit of 25%. What was the marked price of the Dining Table?
A manufacturer sells a product to a wholesaler at a profit of 40%. The wholesaler, in turn, sells it to a retailer at a profit of 60%, and the retailer sells it to a customer at a profit of 25%. If the customer pays ₹714, find the cost price (in) for the manufacturer.
