Question2Question 2Percentage Decrease Module C
For this question, please use your own physical keyboard. You do not need the onscreen keyboard. In a sale, a coat that originally cost £50 is reduced by 30 %. What is the sale price of the coat? Enter your answer: £Invalid input. Enter a numerical value.[input] Please note: You do not need to use the on-screen keyboard to enter your answer for this question or similar ones. You may input your response directly using your physical keyboard or standard input method. Maximum marks: 3 Flag question undefined

Question

BlackTom AI · Accepted Answer

Reducing a price by 30% is equivalent to keeping 70% of the original price, so the sale price is 70% of £50.

1. Relevant knowledge points and concepts
- Percentage decrease: a reduction of p% means the new amount = original × (1 − p/100).
- Converting percentages to decimals: 30% = 30/100 = 0.30; remaining proportion = 1 − 0.30 = 0.70.

2. Complete step-by-step reasoning
Method A (subtract the decrease):
- Find the amount of the decrease: 30% of £50.
- Subtract that decrease from the original price to get the sale price.

Method B (use the remaining proportion directly):
- Multiply the original price by 70% (0.70) to get the sale price in one step.

3. Calculations with intermediate steps
Method A:
- 30% of £50 = 30/100 × 50 = 0.30 × 50 = 15.
- Sale price = original − decrease = 50 − 15 = 35.

Method B:
- Sale price = 50 × (1 − 0.30) = 50 × 0.70 = 35.

4. Why the correct answer is correct
Both methods give the same result because reducing by 30% removes 30% of the original value (15) and leaves 70% (35). Multiplying by 0.70 directly captures the remaining proportion and yields £35.

5. Common incorrect answers and why they are wrong
- £65 would be wrong if someone mistakenly added 30% instead of subtracting it (50 + 15).
- £15 would be wrong if someone reported only the amount removed (the discount) rather than the sale price.
- Any result like £49.70 would be a miscalculation of the percentage conversion.

6. Conclusion
The sale price after a 30% reduction on £50 is £35, which matches the provided correct answer (35).

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