Exercise: Percentage
Questions for: Simple Percentage
A local bakery produced 400 loaves of bread last week. This week, due to increased demand, their production increased by 20%.
What was the total number of loaves produced this week?
A: 420
B: 440
C: 480
D: 500
Answer: C
1. The initial production was 400 loaves.
2. The production increased by 20%.
3. Calculate the amount of the increase: 20% of 400 = (20/100) * 400.
4. Simplify the calculation: 0.20 * 400 = 80 loaves.
5. Add the increase to the original production to find the total for this week: 400 + 80 = 480 loaves.
Why others are wrong:
A — This result would occur if the increase was incorrectly calculated as 20 absolute units instead of 20 percent of the original amount.
B — This result would occur if the increase was incorrectly calculated, possibly as 10% of 400 (40 loaves) instead of 20%.
D — This result would occur if the increase was incorrectly calculated as 25% of 400 (100 loaves), or a similar miscalculation.
A factory's monthly output of specific components was 500 units in January. In February, output increased by 10% compared to January. However, in March, output decreased by 5% compared to February's output.
What percentage of January's output was March's output?
A: 104.5%
B: 105%
C: 102.5%
D: 95%
Answer: A
1. Calculate January's output: 500 units.
2. Calculate February's output: 10% increase from January.
10% of 500 = 0.10 * 500 = 50 units.
February's output = 500 + 50 = 550 units.
3. Calculate March's output: 5% decrease from February.
5% of 550 = 0.05 * 550 = 27.5 units.
March's output = 550 - 27.5 = 522.5 units.
4. Calculate March's output as a percentage of January's output:
(March's output / January's output) * 100
(522.5 / 500) * 100 = 1.045 * 100 = 104.5%.
Why others are wrong:
A — Correct.
B — Incorrect calculation, likely by applying the 5% decrease to the original January output (550 - 25 = 525; 525/500 = 105%) or assuming a net 5% increase (10% - 5% = 5%).
C — Incorrect calculation, possibly from averaging percentage changes or other miscalculation.
D — Incorrect calculation, likely only considering the 5% decrease relative to the original January output and ignoring the initial increase.
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A local bookstore implemented a sales promotion, reducing the price of all fiction novels by 20%. A customer purchased a novel for $18 during this promotion.
What was the original price of the novel before the discount?
A: $21.60
B: $22.50
C: $20.00
D: $24.00
Answer: B
1. The novel was purchased for $18 after a 20% discount.
2. This means that $18 represents 100% - 20% = 80% of the original price.
3. Let 'X' be the original price of the novel.
4. So, 0.80 * X = $18.
5. To find X, divide $18 by 0.80.
6. X = 18 / 0.80 = $22.50.
Why others are wrong:
A — This value is obtained by calculating 20% of $18 and adding it to $18, incorrectly assuming $18 is the original price.
C — This value would imply a discount of $2 from an original price of $20, which is a 10% discount, not 20%.
D — This value would be the original price if the $18 represented a 25% discount (18 / 0.75 = 24), not a 20% discount.
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A local bookstore sold 350 copies of a popular novel last month. This month, their sales of the same novel increased by 14%.
How many copies of the novel did the bookstore sell this month?
A: 399
B: 49
C: 336
D: 385
Answer: A
Step 1: Calculate the increase in sales.
Increase = 14% of 350 copies
Increase = (14/100) * 350
Increase = 0.14 * 350
Increase = 49 copies
Step 2: Add the increase to the original sales to find the new total.
New sales = Original sales + Increase
New sales = 350 + 49
New sales = 399 copies
Why others are wrong:
A — This is the correct total number of copies sold after the increase.
B — This represents only the absolute increase in sales, not the total number of copies sold this month.
C — This would be an incorrect decrease, implying the sales went down, and the value itself (350 - 14) does not correspond to a 14% decrease.
D — This might result from calculating a 10% increase (350 + 35 = 385) instead of a 14% increase.
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A high-end espresso machine's price was reduced by 15% during a clearance sale. Its new selling price is $425.
What was the original price of the espresso machine before the sale?
A: $488.75
B: $500.00
C: $361.25
D: $475.00
Answer: B
1. Let the original price be P.
2. A 15% reduction means the new price is 100% - 15% = 85% of the original price.
3. So, 0.85 * P = $425.
4. To find P, divide the new price by 0.85.
5. P = $425 / 0.85 = $500.
Why others are wrong:
A — This calculation incorrectly adds 15% of the *new* price ($425) to $425 (i.e., $425 * 1.15).
B — This is the correct answer.
C — This calculation incorrectly subtracts 15% of the *new* price ($425) from $425 (i.e., $425 * 0.85).
D — This option is not derived from correct percentage calculation and likely results from a miscalculation or approximation.
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