A car dealer advertises a 20% discount on his cars. Then, a 10% tax is added to the discounted price. If the final price is 7040BD, what was the car’s price before the discount?
The correct answer and explanation is:
To find the original price of the car before any discount or tax, we can work backward from the final price of 7040 BD.
Step 1: Understand the pricing steps
- The original price is discounted by 20%, so the buyer pays 80% of the original price.
- Then a 10% tax is added to that discounted price, so the final price is 110% of the discounted price.
- The final amount after tax is 7040 BD.
Let the original price be x BD.
Step 2: Set up the equation
- After the 20% discount:
Discounted price = 0.80 × x - After adding 10% tax:
Final price = 1.10 × (0.80 × x) = 7040
Step 3: Solve for x
1.10×0.80×x=70401.10 × 0.80 × x = 7040 0.88×x=70400.88 × x = 7040 x=70400.88=8000x = \frac{7040}{0.88} = 8000
✅ Answer: The original price before discount was 8000 BD
Explanation (300 words)
This problem involves successive percentage changes: a 20% discount followed by a 10% tax. The best way to approach this is to reverse the operations mathematically.
We assume the original price to be x. A 20% discount reduces the price to 80% of x, or 0.80 × x. Then, a 10% tax increases this discounted amount by 10%, which results in multiplying by 1.10. This brings the total final price to: Final Price=1.10×0.80×x=0.88×xFinal\ Price = 1.10 × 0.80 × x = 0.88 × x
Given the final price is 7040 BD, we divide by 0.88 to find the original price: x=7040÷0.88=8000x = 7040 ÷ 0.88 = 8000
Thus, the original price before any discount or tax was 8000 BD.
This type of problem demonstrates the importance of understanding percentage operations. Discounts and taxes do not cancel each other out directly because they’re applied to different base amounts. Always apply each percentage step-by-step, and when solving backward, reverse the operations in order. This helps in real-life shopping, budgeting, and financial literacy scenarios.