Profit

Question 1: If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?

Question 2: Sam buys 10 apples for $1. At what price should he sell a dozen apples if he wishes to make a profit of 25%?

Question 3: By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What will be the % profit made by the merchant if he sells the article at 95% of its marked price?

Question 4: What is the maximum percentage discount that a merchant can offer on her Marked Price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?

Question 5: A merchant who marked his goods up by 50% subsequently offered a discount of 20%. What is the percentage profit that the merchant make after offering the discount? 

Answers:

1.Let the cost price of 1 article be $1.

Therefore, cost price of 20 articles = 20 * 1 = $20

The selling price of 25 articles = cost price of 20 articles = $20.

Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.

Cost price of 25 articles = 25 * 1 = $25.

Therefore, profit made on sale of 25 articles = Selling price of 25 articles - cost price of 25 articles

= 20 - 25 = -$5.

As the profit is in the negative, the merchant has made a loss of $5. 

Therefore, % loss = 
% loss =  = 20% loss.

2.The cost price of 1 apple = th of a dollar or $0.10.

As Sam wishes to make a profit of 25%, his selling price per apple will be 0.10 + 25% of 0.10 = $0.125.

If the selling price of 1 apple is $0.125, then the selling price of a dozen apples = 12 * 0.125

= $1.5

3.Let the marked price be S and the cost price of the article be C

When the merchant sells at 80% of marked price he sells at 0.8S

This results in a loss of 12%.

Loss is always computed as a percentage of cost price.

Therefore, the loss incurred by the merchant = 0.12C

Hence, he will be selling the article at C - 0.12C = 0.88C when he sells at 80% of his marked price.

Equating the two sides of the relation, we get 0.8S = 0.88C

Or S = 

Or S = 1.1C

Now, if the merchant sells at 95% of the marked price, he will be selling at 95% of 1.1C = 1.045C

Hence, the merchant will make a profit of 4.5%.

4.The merchant had initially marked her goods up by 50%.

Let us assume that her cost price of the goods to be $ 100.

Therefore, a 50% mark up would have resulted in her marked price being $100 + 50% of $100 = $100 + $50 = $150.

The question states that she finally sells the product at no profit or loss. This essentially, means that she sells the product at cost price, which in this case would be $100.

Therefore, she had offered a discount of $50 on her marked price of $150.

Hence, the % discount offered by her =  = 33.33%.

5.The easiest way to solve these kinds of problems is to assume a cost price for the merchant.

To make calculations easy, let us assume that the cost price = $100

The merchant marks his goods up by 50%.

Therefore, his quoted price = cost price + mark up

= $100 + 50% of $100 = 100 + 50 = $150

Now, the merchant offers a discount of 20% on his quoted price

Therefore, amount of discount = 20% of $150 = 20% of 150 = $30

Therefore, he finally sells it for $150 - $30 = $ 120.

We assumed his cost to be $ 100 and he sold it finally for $ 120.

Therefore, his net profit = $ 20 on his cost of $ 100

Hence, his % profit =  = 20%.