Exercise: Percentage

Questions for: Simple Percentage

A shop had 400 units of a product in stock. On Monday, 25% of the stock was sold. On Tuesday, 10% of the *remaining* stock was sold. How many units of the product were sold in total over Monday and Tuesday?
A: 130
B: 100
C: 140
D: On Tuesday, 10% of the *remaining* stock was sold. How many units of the product were sold in total over Monday and Tuesday? A. 130 B. 100 C. 140 D. 270
Answer: A
1. Calculate units sold on Monday: 25% of 400 units = 0.25 * 400 = 100 units. 2. Calculate remaining units after Monday's sales: 400 - 100 = 300 units. 3. Calculate units sold on Tuesday: 10% of the remaining 300 units = 0.10 * 300 = 30 units. 4. Calculate total units sold over Monday and Tuesday: 100 units (Monday) + 30 units (Tuesday) = 130 units. Why others are wrong: A — Correct. B — This is only the number of units sold on Monday, not the total for both days. C — This would be the result if Tuesday's sales were calculated as 10% of the *original* 400 units (40 units), then added to Monday's sales (100 + 40 = 140). D — This is the number of units remaining after both days of sales (400 - 130 = 270), not the total number sold.
A factory produced 250 toy cars. During quality control, it was determined that 12% of the cars had minor defects and could not be sold. How many toy cars were suitable for sale?
A: 30
B: 220
C: 238
D: How many toy cars were suitable for sale? A. 30 B. 220 C. 238 D. 200
Answer: B
1. Identify the total number of toy cars produced: 250. 2. Calculate the number of defective cars: 12% of 250. 3. Convert the percentage to a decimal: 12% = 0.12. 4. Multiply the total by the decimal: 0.12 * 250 = 30. So, 30 cars were defective. 5. Subtract the number of defective cars from the total number of cars to find those suitable for sale: 250 - 30 = 220. Why others are wrong: A — This represents the number of defective cars, not the number suitable for sale. C — This is the result of incorrectly subtracting the percentage value (12) directly from the total (250 - 12 = 238), rather than calculating 12% of the total. D — This would be the result if 20% of the cars were defective (250 - 50 = 200), or if 80% of the cars were suitable, which is incorrect for a 12% defect rate.
A sweater is on sale for $72 after a 20% discount has been applied to its original price. What was the original price of the sweater before the discount?
A: $86.40
B: $90.00
C: $92.00
D: $80.00
Answer: B
1. A 20% discount means the sale price represents 100% - 20% = 80% of the original price. 2. Let the original price be 'P'. 3. So, 0.80 * P = $72. 4. To find the original price, divide the sale price by 0.80. 5. P = $72 / 0.80 = $90. Why others are wrong: A — This would be the result of calculating 20% of the sale price ($72) and adding it back ($72 + $14.40 = $86.40), which is an incorrect method for finding the original price. B — (Correct answer) C — This would be the result of assuming a fixed reduction of $20 from the original price ($72 + $20 = $92), rather than a percentage discount. D — This might arise from a miscalculation, such as incorrectly assuming the $72 represents 90% of the original price (72 / 0.90 = $80), implying a 10% discount instead of 20%.
A warehouse received a shipment of 500 laptops. 20% of the laptops were immediately marked as "premium" and separated. From the *remaining* laptops, 15% were found to have minor cosmetic damage during an initial check. What percentage of the *original* shipment of laptops consists of non-premium laptops without cosmetic damage?
A: 68%
B: 65%
C: 70%
D: From the *remaining* laptops, 15% were found to have minor cosmetic damage during an initial check. What percentage of the *original* shipment of laptops consists of non-premium laptops without cosmetic damage? A. 68% B. 65% C. 70% D. 80%
Answer: A
1. The original shipment represents 100% of the laptops. (The specific number 500 is not needed for this percentage calculation.) 2. 20% of the laptops were marked "premium", meaning 100% - 20% = 80% remained as non-premium. 3. Of these *remaining* 80%, 15% were found to have minor cosmetic damage. 4. Calculate 15% of 80%: 0.15 * 80% = 12%. 5. These 12% represent the non-premium laptops with cosmetic damage. 6. To find the percentage of non-premium laptops *without* cosmetic damage, subtract this 12% from the 80% that were non-premium: 80% - 12% = 68%. Why others are wrong: A — Correct. B — Incorrectly subtracts the percentages sequentially from the original total (100% - 20% - 15% = 65%), rather than calculating the second percentage based on the remainder. C — This result would be obtained by incorrectly assuming the defect rate was 10% of the remainder (80% - 10% = 70%). D — This result (80%) only accounts for the initial 20% being marked as premium and ignores the subsequent 15% cosmetic damage from the remaining laptops.
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