Sure! Let's break this down step-by-step to solve this problem.
### Initial Information:
- Initial price of the goods: \[tex]$200
- Trade discount rate: 30%
- Promotional discount rate: 20%
### Step 1: Calculate the price after applying the trade discount
1. Trade discount calculation:
- Trade discount amount = Initial price * Trade discount rate
- Trade discount amount = $[/tex]200 * 0.30 = [tex]$60
2. Price after trade discount:
- Price after trade discount = Initial price - Trade discount amount
- Price after trade discount = $[/tex]200 - [tex]$60 = $[/tex]140
### Step 2: Calculate the price after applying the promotional discount to the reduced price
1. Promotional discount calculation:
- Promotional discount amount = Price after trade discount Promotional discount rate
- Promotional discount amount = [tex]$140 0.20 = $[/tex]28
2. Price after promotional discount:
- Final price = Price after trade discount - Promotional discount amount
- Final price = [tex]$140 - $[/tex]28 = [tex]$112
### Step 3: Calculate the equivalent discount rate
1. Equivalent discount rate calculation:
- Equivalent discount rate is the total discount as a fraction of the initial price.
- Equivalent discount amount = Initial price - Final price
- Equivalent discount amount = $[/tex]200 - [tex]$112 = $[/tex]88
2. Equivalent discount rate:
- Equivalent discount rate = Equivalent discount amount / Initial price
- Equivalent discount rate = [tex]$88 / $[/tex]200 = 0.44 or 44%
### Summary
1. The retailer would pay \[tex]$112 for $[/tex]200 worth of goods after applying both the trade and promotional discounts.
2. The equivalent discount rate is 44%.
Hence, the detailed and step-by-step solution verifies:
1. [tex]\( \$112 \)[/tex]
2. [tex]\( 44\% \)[/tex]
