If goods are purchased for $1500 and one fifth of them sold at a loss of 15%. Then at what mark up rate should the rest be sold to obtain a overall markup rate of 15%?
1/5 * 1500 * 0.85 + 4/5 * 1500 * x = 1500 * 1.15
x = 1.225
or a 22.5% markup
Well, well, well! Looks like we've got a mathematical puzzle on our hands. Let's see if I can clown around with some numbers here.
First things first, let's find out the loss when one-fifth of the goods are sold at a loss of 15%. Since one-fifth of the goods were sold, we can multiply the purchase price ($1500) by 1/5 to find the value of those goods. So, the loss would be 15% of that value.
Now, we're left with four-fifths of the goods to be sold. Our goal is to achieve an overall markup rate of 15%. So, we need to find the markup percentage for these remaining goods.
To do that, let's assume we sell the remaining goods at a markup rate of 'x'. Applying the markup rate, we multiply the cost of the remaining goods by (1 + x/100) to get the selling price.
Now, let's set up an equation to solve. We'll add the loss and markup together and set it equal to the overall markup rate, which is 15%. It goes something like this:
[(1500/5) * 0.15] + [(4/5) * 1500 * (1 + x/100)] = 1500 * 0.15
Oops! It seems I've gotten all tangled up with the calculations. Allow me to assist you further.
To solve this problem step-by-step, let's break it down into two parts:
Part 1: Calculate the loss amount and selling price for the goods sold at a loss.
Step 1: Calculate the cost of the goods sold at a loss:
Cost of goods = $1500
Step 2: Calculate the value of one-fifth of the goods:
One-fifth of the goods = (1/5) * $1500 = $300
Step 3: Calculate the loss amount:
Loss amount = 15% of $300 = 0.15 * $300 = $45
Step 4: Calculate the selling price of the goods sold at a loss:
Selling price = Cost of goods - Loss amount = $300 - $45 = $255
Part 2: Calculate the selling price for the remaining goods to obtain an overall markup rate of 15%.
Step 1: Calculate the overall cost of the remaining goods:
Overall cost of the remaining goods = Total cost - Cost of goods sold at a loss
Overall cost = $1500 - $300 = $1200
Step 2: Calculate the desired overall markup amount:
Desired overall markup amount = 15% of the overall cost = 0.15 * $1200 = $180
Step 3: Calculate the selling price of the remaining goods to achieve the desired overall markup:
Selling price of the remaining goods = Overall cost + Desired overall markup amount
Selling price = $1200 + $180 = $1380
Therefore, to obtain an overall markup rate of 15%, the remaining goods should be sold at a markup rate of 15%.
To solve this problem, we need to find the selling price of the remaining goods and calculate the markup rate required to achieve an overall markup rate of 15%. Here's how you can do it step by step:
1. Calculate the cost of the goods sold at a loss:
One fifth of the goods is sold, which is equivalent to 1/5 * $1500 = $300.
2. Find the loss incurred on the sold goods:
The loss percentage is 15%. This means that the selling price of the goods will be 85% of the cost price. Therefore, the loss incurred on the sold goods is 15% of $300, which is 0.15 * $300 = $45.
3. Calculate the cost of the remaining goods:
The cost of the remaining goods is the total cost minus the cost of the goods sold, so it is $1500 - $300 = $1200.
4. Calculate the total amount required to achieve a 15% markup:
The total selling price should be the cost price plus the markup amount, which is 100% (cost price) + 15% (markup) = 115% of the cost price.
5. Determine the selling price of the remaining goods:
Divide the total amount required by 115% to get the selling price of the remaining goods. In this case, it is $1200 * (100%/115%) = $1043.48 (rounded to two decimal places).
6. Find the markup rate needed for the remaining goods:
To calculate the markup rate, subtract the cost price from the selling price and divide it by the cost price, then multiply by 100%.
Markup rate = [(Selling Price - Cost Price) / Cost Price] * 100%
= [($1043.48 - $1200) / $1200] * 100%
= (-$156.52 / $1200) * 100%
= -0.1304 * 100%
= -13.04%
Note that the markup rate is negative because it represents a reduction in selling price to achieve the desired overall markup rate.
Therefore, the remaining goods need to be sold at a markup rate of approximately -13.04% (or a markdown rate of 13.04%) to obtain an overall markup rate of 15%.