A manufacturer offers a 11% discount on the marked price of a product. The retailer offers another 20% on the reduced price. By what single number would you need to multiply the marked price to get the retail price of the product?
The correct answer and explanation is:
Correct Answer: 0.712
Step-by-Step Explanation:
When multiple percentage discounts are applied sequentially, we can calculate the final price as a fraction of the original (marked) price by multiplying the two discounts together in decimal form.
Let’s walk through it:
Step 1: First Discount (Manufacturer’s Discount)
- Manufacturer offers an 11% discount on the marked price.
- This means the customer now pays 89% of the marked price: New price after first discount=100%−11%=89%=0.89\text{New price after first discount} = 100\% – 11\% = 89\% = 0.89
Step 2: Second Discount (Retailer’s Discount)
- Retailer offers a 20% discount on the already reduced price.
- The customer now pays 80% of this reduced price: New price after second discount=100%−20%=80%=0.80\text{New price after second discount} = 100\% – 20\% = 80\% = 0.80
Step 3: Combine the Two Discounts
- Multiply the two decimal values: Final Price=0.89×0.80=0.712\text{Final Price} = 0.89 \times 0.80 = 0.712
Conclusion:
The retail price is 71.2% of the marked price.
Thus, to get the final retail price from the marked price directly, you multiply the marked price by: 0.712\boxed{0.712}
Interpretation:
This number, 0.712, is a single multiplier that reflects the combined effect of two successive discounts:
- The first discount brings down the price a little,
- Then the second discount cuts that already-reduced price further.
This kind of problem is common in real-world pricing scenarios like store sales or bulk discounts, and understanding how to combine discounts using multiplication helps avoid mistakes like adding them directly (which would give a wrong result of 31% discount instead of the true 28.8% discount represented by 0.712).