Calculating Net Gain or Loss on Shirts
This problem involves calculating the total profit or loss when two items are sold at the same price but with different profit and loss percentages.
Step 1: Calculate Cost Price (CP) for the First Shirt (25% Gain)
Selling Price (SP) = Rs. 500
Gain = 25%
The formula relating SP, CP, and Gain is: $SP = CP \times (1 + \frac{Gain \%}{100})$
Substituting the values: $500 = CP_1 \times (1 + \frac{25}{100})$ $500 = CP_1 \times (1.25)$ $CP_1 = \frac{500}{1.25}$ $CP_1 = 400$ The cost price of the first shirt is Rs. 400.
Step 2: Calculate Cost Price (CP) for the Second Shirt (25% Loss)
Selling Price (SP) = Rs. 500
Loss = 25%
The formula relating SP, CP, and Loss is: $SP = CP \times (1 - \frac{Loss \%}{100})$
Substituting the values: $500 = CP_2 \times (1 - \frac{25}{100})$ $500 = CP_2 \times (0.75)$ $CP_2 = \frac{500}{0.75}$ $CP_2 = \frac{500}{\frac{3}{4}}$ $CP_2 = \frac{500 \times 4}{3}$ $CP_2 = \frac{2000}{3}$ The cost price of the second shirt is Rs. $\frac{2000}{3}$.
Step 3: Calculate Total Selling Price
Total SP = SP of Shirt 1 + SP of Shirt 2
Total SP = $500 + 500 = 1000$
The total selling price is Rs. 1000.
Step 4: Calculate Total Cost Price
Total CP = CP of Shirt 1 + CP of Shirt 2
Total CP = $400 + \frac{2000}{3}$ Total CP = $\frac{400 \times 3}{3} + \frac{2000}{3}$ Total CP = $\frac{1200}{3} + \frac{2000}{3}$ Total CP = $\frac{3200}{3}$ The total cost price is Rs. $\frac{3200}{3}$.
Step 5: Determine Net Gain or Loss
Compare Total CP and Total SP:
Total CP = $\frac{3200}{3} \approx 1066.67$
Total SP = $1000$
Since Total CP > Total SP, there is a net loss.
Net Loss = Total CP - Total SP
Net Loss = $\frac{3200}{3} - 1000$ Net Loss = $\frac{3200}{3} - \frac{3000}{3}$ Net Loss = $\frac{200}{3}$
Converting the fraction to a decimal: Net Loss $\approx 66.67$
The shopkeeper has a net loss of approximately Rs. 66.67.
Similar Questions
- A furniture establishment initially disposes of a particular dining table for ₹X, thereby realizing a 25% profit margin. Subsequently, as a promotional strategy for a festive period, the marked price of this identical table is elevated to ₹Y. Following this adjustment, a special concession of 20% is applied to the newly established marked price. The inquiry then seeks to ascertain the resulting percentage profit generated by the store during this specific celebratory sales period. What is the percentage profit earned by the store during the festive sale?
- A software company developed 800 licenses for a new application at a total cost of ₹4,000,000. They provided 50 licenses free to their top beta testers. For the remaining licenses, they offered a 15% discount on the market price of ₹6000 per license. Additionally, they gave 1 license free for every 9 licenses bought. If all 800 licenses were distributed, what is the company's overall gain or loss percentage?
- A wholesaler sells a packet of tea to a retailer at a profit of 20%. The retailer then marks up the price by 50% and offers a discount of 20% to the customer. If the customer pays Rs. 480, find the cost price of the packet for the wholesaler.
- A bakery produced 5000 cakes at a total cost of ₹250,000. They gave away 500 cakes for a promotional event. For the remaining cakes, they offered a 20% discount on the market price of ₹75 per cake. Additionally, they gave one cake free with every 9 cakes bought. If all 5000 cakes were distributed, what is their overall gain or loss percentage?
- An electronics store orders 150 portable speakers at a cost of ₹400 each. The owner plans to price them so that selling only 120 speakers would guarantee a 40% profit on the total investment. However, a local event leads to the sale of 135 speakers. If the remaining speakers have no resale value, calculate the store's actual profit percentage on the total investment.
- A seller offers a 40% discount on an item whose cost price is Rs. 720. Despite the discount, the seller earns a profit of 20%. What must be the marked price?
- If the cost price of 15 articles is equal to the selling price of 12 articles, what is the profit percent?
- An electronics dealer marks an item 60% above cost and offers a festival discount of 25%, plus a cashback of Rs. 300 on the final selling price. If he still makes a 10% profit, what is the cost price?
- A man buys a set of 3 identical watches at a total cost of Rs. 4,500. He sells them at Rs. 1,800, Rs. 1,700, and Rs. 1,600, respectively. What is the overall profit or loss?
- A trader marks his goods 40% above the cost price and gives a discount of 25%.
If he gains Rs. 75 on an item, what is the cost price of the item?
Important Questions from Profit and Loss
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?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
