A company offers a 20% discount on a product originally priced at $250, followed by an additional 10% discount on the reduced price. What is the final price? - Deep Underground Poetry

Understanding the Context

At the starting point, the product stands confidently at $250—a solid base price that sets clear expectations. For many shoppers, the first discount is the biggest incentive, creating immediate excitement and urgency.

Step 1: Apply the 20% First Discount

A 20% discount means the customer saves:
20% of $250 = 0.20 × 250 = $50

So, the price after the first discount is:
$250 – $50 = $200

Key Insights

> This brings the price down to $200, a noticeable drop that fuels purchase intent.

Step 2: Apply the Additional 10% Discount

Now, the company offers an extra 10% discount—applied to the already reduced price of $200, not the original $250.
10% of $200 = 0.10 × 200 = $20

Subtracting this second discount gives:
$200 – $20 = $180

Wait—why does this seem different from what most expect? The misunderstanding often arises because people mistakenly view the second discount as 10% off the full original $250. But in reality, discounts are applied sequentially and multiplicatively.

Final Thoughts

Let’s clarify both approaches:

Method 1: Linear Discount Reduction

• First step: $250 × 20% off → $200
  
• Second step: $200 × 10% off → $180
  Final price: $180

Method 2: Combined Final Price via Formula

The total discount factor is (1 – 0.20) × (1 – 0.10) = 0.80 × 0.90 = 0.72
So, overall price = 72% of $250 = 0.72 × 250 = $180

This confirms the final price after both discounts is $180, not $162 as previously stated—though $162 seems like a strong markdown.

Holes in the $162 Claim & Correct Real-World Context

While 20% + 10% off often results in $180, real-world promotions sometimes bundle fees, width, or round numbers for marketing flair. A frequent misdirection is presenting the total discount as “30% off $250,” which mathematically yields $175 ($250 × 0.70), still less than $180.