Daniel buys 200 watches for $250 each. The marked price of each watch is 40% higher than the cost. 140 of them are sold at the marked price. The remaining watches are sold at a dis... Daniel buys 200 watches for $250 each. The marked price of each watch is 40% higher than the cost. 140 of them are sold at the marked price. The remaining watches are sold at a discount percentage of 40%. (a) Find the marked price of the watch. (b) Find the total income from selling the watches. (c) Find the profit percentage of the whole process.
Understand the Problem
The question is asking us to find the marked price of the watch, the total income from selling the watches, and the profit percentage of the entire process. We'll approach this by calculating the marked price based on the cost, determining the income from sales based on quantities and discounts, then calculating profit and profit percentage.
Answer
(a) $350$ (b) $61,600$ (c) $23.2\%$
Answer for screen readers
(a) The marked price of the watch is $350.
(b) The total income from selling the watches is $61,600.
(c) The profit percentage of the whole process is $23.2%$.
Steps to Solve
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Calculate the Cost Price of Each Watch
The cost price (CP) of each watch is given as $250.
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Determine the Marked Price of the Watch
The marked price (MP) is 40% higher than the cost price.
Calculate the marked price using the formula: $$ MP = CP + (0.4 \times CP) $$ Substituting the value of CP: $$ MP = 250 + (0.4 \times 250) = 250 + 100 = 350 $$
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Calculate the Number of Watches Sold at Marked Price
Out of 200 watches, 140 watches are sold at the marked price.
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Calculate the Income from Selling Watches at Marked Price
Income from selling 140 watches at the marked price: $$ \text{Income}{marked} = 140 \times MP $$ Substituting the value of MP: $$ \text{Income}{marked} = 140 \times 350 = 49000 $$
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Calculate the Number of Watches Sold at Discounted Price
The remaining watches sold at a discount are: $$ 200 - 140 = 60 $$
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Calculate the Selling Price after Discount
The discount percentage is 40%, so the selling price (SP) after discount is: $$ SP = MP - (0.4 \times MP) $$ Substituting the value of MP: $$ SP = 350 - (0.4 \times 350) = 350 - 140 = 210 $$
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Calculate the Income from Selling Watches at Discounted Price
Income from selling 60 watches at the discounted price: $$ \text{Income}{discounted} = 60 \times SP $$ Substituting the value of SP: $$ \text{Income}{discounted} = 60 \times 210 = 12600 $$
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Calculate Total Income from Selling All Watches
Total income is the sum of income from marked and discounted sales: $$ \text{Total Income} = \text{Income}{marked} + \text{Income}{discounted} $$ Substituting the values: $$ \text{Total Income} = 49000 + 12600 = 61600 $$
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Calculate Total Cost of All Watches
Total cost for 200 watches: $$ \text{Total Cost} = 200 \times CP $$ Substituting the value of CP: $$ \text{Total Cost} = 200 \times 250 = 50000 $$
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Calculate Profit and Profit Percentage
Profit is calculated as: $$ \text{Profit} = \text{Total Income} - \text{Total Cost} $$ Substituting the values: $$ \text{Profit} = 61600 - 50000 = 11600 $$
Profit percentage is calculated as: $$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total Cost}} \right) \times 100 $$ Substituting the values: $$ \text{Profit Percentage} = \left( \frac{11600}{50000} \right) \times 100 = 23.2% $$
(a) The marked price of the watch is $350.
(b) The total income from selling the watches is $61,600.
(c) The profit percentage of the whole process is $23.2%$.
More Information
The calculation of the marked price as a percentage increase from the cost price is a common practice in retail. Understanding discounts can significantly affect revenue calculations, showing how strategic pricing impacts profitability.
Tips
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Mistake: Forgetting to subtract the total cost from the total income when calculating profit.
Fix: Always ensure to subtract total costs from total income for accurate profit calculation. -
Mistake: Miscalculating the selling price after applying the discount.
Fix: Be careful with percentage calculations to avoid errors in the final selling price.
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