Problem Analysis
The question asks for the original cost price (CP) for the wholesaler. We are given a chain of transactions involving profit, markup, and discount, leading to a final customer price. We need to work backward from the final price to find the initial cost.
Step-by-Step Solution
- Define Variables: Let the wholesaler's cost price be $C_{W}$.
- Wholesaler to Retailer Transaction: The wholesaler sells to the retailer at a 20% profit. Retailer's Cost Price ($C_{R}$) = Wholesaler's Selling Price ($S_{W}$) = $C_{W} \times (1 + \frac{20}{100}) = 1.20 \times C_{W}$.
- Retailer Markup: The retailer marks up the price by 50%. Retailer's Marked Price ($M_{R}$) = $C_{R} \times (1 + \frac{50}{100}) = 1.20 \times C_{W} \times 1.50 = 1.80 \times C_{W}$.
- Retailer Discount: The retailer offers a 20% discount on the marked price. Retailer's Selling Price ($S_{R}$) = $M_{R} \times (1 - \frac{20}{100}) = 1.80 \times C_{W} \times 0.80 = 1.44 \times C_{W}$.
- Final Customer Price: The customer pays Rs. 480, which is the retailer's selling price. So, $S_{R} = 480$.
- Calculate Wholesaler's Cost Price: We have the equation: $1.44 \times C_{W} = 480$. Solving for $C_{W}$: $C_{W} = \frac{480}{1.44}$ $C_{W} = \frac{480}{\frac{144}{100}} = \frac{480 \times 100}{144}$ $C_{W} = \frac{48000}{144}$ $C_{W} = \frac{1000}{3}$ $C_{W} \approx 333.33$
Therefore, the cost price of the packet for the wholesaler is Rs. 333.33.
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By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
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