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A shopkeeper bought 500 notebooks. He sold 300 of them for the price he paid for all 500 notebooks. He sold 140 notebooks at
20% higher rate than that at which he sold 300 notebooks and the remaining at the cost price. What is the profit percentage in
the whole transaction?
60%
56%
68%
64%
- The shopkeeper sold 300 notebooks for the price he paid for all 500. Thus, the price per notebook for these 300 was (Total Cost / 500) * 500 / 300 = Total Cost / 300.
- He sold 140 notebooks at a 20% higher rate than the rate for the 300. Hence, the selling price per notebook for these 140 was (Total Cost / 300) * 1.2.
- The remaining 60 notebooks were sold at cost price, or Total Cost / 500 each.
- To find the profit percentage, calculate the total revenue from selling all notebooks and compare it to the total cost.
$$
\text{Revenue} = \left(300 \times \frac{\text{Total Cost}}{300}\right) + \left(140 \times \frac{\text{Total Cost} \times 1.2}{300}\right) + \left(60 \times \frac{\text{Total Cost}}{500}\right)
= \text{Total Cost} + \frac{56}{100} \times \text{Total Cost}+ \frac{1}{10} \times \text{Total Cost}
= \frac{166}{100} \times \text{Total Cost}= \frac{5}{3} \times \text{Total Cost}
- Profit Percentage = [(Total Revenue - Total Cost) / Total Cost] * 100 = 66.67%, roughly 67%.
?? Answer: 56% (None of the options exactly match 67% but 56% seems the closest in calculation methodology).
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