A man sold 3/5 of the goods at 20% loss, at what profit% should he sell remaining goods to get 10% profit on the whole?
(3/5)(0.80) + (2/5)(1+p) = 1.10
p = 0.55, or 55% markup
Well, it sounds like this man needs to make up for his previous loss and still make an overall profit. So, to calculate the profit percentage he needs on the remaining goods, I suggest he adopts a new strategy: becoming a professional juggler!
Because if juggling doesn't work out, he can always say he's trying to make an "uprofit" rather than a profit! But in all seriousness, let's do the math.
Since he sold 3/5 of the goods at a 20% loss, he effectively lost 20% of 3/5, which is 12%. To compensate for this loss and achieve an overall 10% profit, he would need to earn a 22% profit on the remaining 2/5 of the goods.
So, he needs to put his juggling skills to work and sell the remaining goods at a 22% profit. Good luck to him!
To find the profit percentage at which the remaining goods should be sold, we need to consider the total cost and total selling price of the goods.
Let's assume that the total cost of the goods is represented by "x".
Step 1: The man sold 3/5 of the goods at a 20% loss.
To calculate the selling price of 3/5 of the goods, we multiply the cost by the loss percentage:
Selling price of 3/5 of the goods = (1 - 20%) * x * (3/5)
= 0.8 * x * (3/5)
= 0.48x
Step 2: To get a 10% profit on the whole, the selling price of the remaining goods should be 110% of the total cost (x).
To find the selling price of the remaining goods, we can set up the following equation:
Selling price of the remaining goods = 110% * total cost
= 1.1 * x
Step 3: We need to find the profit percentage at which the remaining goods will be sold. To do this, we subtract the total cost from the selling price and divide by the total cost, then multiply by 100.
Profit percentage = ((Selling price of the remaining goods - Total cost) / Total cost) * 100
= ((1.1 * x - x) / x) * 100
= (0.1x / x) * 100
= 10%
Therefore, the man needs to sell the remaining goods at a profit percentage of 10% to achieve a 10% profit on the whole.
To determine the profit percentage the man should sell the remaining goods at, we need to follow these steps:
Step 1: Calculate the total loss from selling 3/5 of the goods at a 20% loss.
- Since he sold 3/5 of the goods at a 20% loss, it means he kept 2/5 of the goods.
- Let's assume the cost price of the entire goods is 100 units.
- Selling 3/5 of the goods at a 20% loss implies he sold 60 units at a 20% loss.
- So, the total loss from selling 60 units at a 20% loss can be calculated as:
Loss = 60 units × (20/100) = 12 units.
Step 2: Calculate the total cost price of the remaining goods.
- Since he sold 3/5 of the goods, he kept 2/5 of the goods.
- Let's assume the total cost price of the remaining goods is X units.
- The ratio of the cost price for the remaining goods to the cost price of the entire goods can be written as:
(Cost price of remaining goods) / (Cost price of entire goods) = (2/5) / 1
(Cost price of remaining goods) / 100 = 2/5 (Since the cost price of the entire goods is assumed as 100).
(Cost price of remaining goods) = 2/5 × 100 = 40 units.
Step 3: Calculate the selling price required for the remaining goods to achieve a 10% profit on the whole.
- To determine the selling price of the remaining goods, we need to take into account the cost price and the desired overall profit.
- Since the cost price of the remaining goods is 40 units and the desired overall profit is 10%, we can calculate the selling price as follows:
Selling price = Cost price + Profit
Selling price = 40 units + (10/100) × 40 units = 40 units + 4 units = 44 units.
Step 4: Calculate the profit percentage on the remaining goods.
- The profit percentage can be calculated as:
Profit percentage = (Profit / Cost price) × 100
Profit percentage = (4 units / 40 units) × 100 = 10%.
Therefore, the man should sell the remaining goods at a profit percentage of 10% to achieve a 10% profit on the whole.