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Profit and Loss Formula, Sample Questions

Profit and Loss

Profit and Loss : Profit and Loss is quite useful in everyday life, apart from that profit and loss is a topic that is asked mostly in the aptitude section of the defense competitive exams, students if you want to secure your marks in the quantitative aptitude then you must learn this topic in detail, you can easily solve the question if you know the concept and understand the Topic thoroughly.

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Profit and Loss : Concepts

Profit:

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. If the selling price of an article is greater than its cost price, there is a gain in the transaction. The basic formula used for calculating the profit is: Profit = Selling Price – Cost Price.

Loss :

When, in a transaction, the cost price is greater than the selling price, it means we incur a loss. If the selling price of an article is lesser than the cost price, there is a loss in the transaction.
The basic formula used for calculating the loss is:
Loss = Cost Price – Selling Price

Cost Price :

The price at which an article is purchased is called its cost price.

Selling Price:

The price at which an article is sold is known as the selling price of the article

Marked Price :

Marked price is the price set by the seller on the label of the article. It is a price at which the seller offers a discount. After the discount is applied on the Marked price, it is sold at a reduced price known as the selling price.

Discount :

To cope with the competition in business and boost the sale of goods, shopkeepers offer discounts to customers. The rebate or the offer given by the shopkeepers to lure the customers is called a discount. Discount is always calculated on the Marked price of the article.

Profit and Loss Examples

  • If you buy a bag for Rs 100 and sell it for Rs 130, the profit is Rs 30.
  • If you buy a bag for Rs 100 and sell it for Rs 80, the loss is Rs 20.
  • If you buy a bag for Rs 100 and sell it for Rs 120, the profit is Rs 20%.

Profit and Loss Formula

  • Profit = SP – CP
  • Loss = CP – SP
  • Profit (%) = {Profit/CP} × 100
  • Loss (%) = {Loss/CP} × 100
  • Discount = Marked Price – Selling Price
  • Discount (%) = (Discount/MP) × 100
  • SP= [(100+ Gain%)/ 100]x CP
  • SP= [(100- Loss%)/ 100]x CP
  • CP= [100/ (100+ Gain%)]x SP
  • CP= [100/ (100- Loss%)]x SP

Profit and Loss: Sample Questions for Defence Exams

Q1. An article is bought for Rs. 675 and sold for Rs. 900. Find the gain percent?

Explanation: 

    • 900 – 675 = 225
    • 225/675*100
    • = 33 1/3%

Q2. A person buys a horse for 15 pounds. After one year, he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the overall profit percent for that person over both the transactions?

Explanation: 

    • Total C.P. = 45
    • Total S.P. = 60
    Profit% = (15/45) *100 = 33.33%

Q2: An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.

Solution:

Gain = SP – CP = 500 – 450 = 50.

Gain% = (50/450)*100 = 100/9 %

Q4. In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?

Solution:

Let us assume CP = Rs. 100.

Then Profit = Rs. 80 and selling price = Rs. 180.

The cost increases by 20% → New CP = Rs. 120, SP = Rs. 180.

Profit % = 60/120 * 100 = 50%.

Therefore, Profit decreases by 30%.

Q5. A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.

Solution:

Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.

Selling price of 8 toys = Rs. 35 → SP of 1 toy = Rs. 35/8

Therefore, Gain = 35/8 – 4 = 3/8.

Gain percent = (3/8)/4 * 100 = 9.375%

Q6. A shopkeeper offers a discount of 20% on the selling price. On a special sale day, he offers an extra 25% off coupon after the first discount. If the article was sold for Rs. 3600, find

  1. The marked price of the article and
  2. The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.

Solution:

Let the marked price of the article be x.

First a 20% discount was offered, on which another 25% discount was offered.

So, 75% of 80% of x = 3600

75/100 * 80/100 * x = 3600 → x = 6000.

So the article was marked at Rs. 6000.

Cost price of the article = [100/(100+80)]*3600 = Rs. 2000.

It is important to note here that this DOES NOT equal to a 45% discount on the whole. When different discounts are applied successively, they CANNOT be added.

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Profit and Loss Formula FAQ

Q1. What is the formula of profit?
Ans. Profit = SP – CP

Q2. What is the formula of Loss?
Ans. Loss = CP – SP

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