Profit, Loss & Discount, Study Notes, Material - All Teaching Exam

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

Selling Price:

The price, at which an article is sold, is called its selling prices, abbreviated as S.P.

• Profit/gain = SP – CP
• Profit % = Profit/(CP)×100
• SP = (100+gain % )/100  ×C P
• CP = 100/(100+gain %)×S P

Loss:

If the overall Cost Price exceeds the selling price of the buyer then he is said to have incurred loss.

• Loss = C P – S P
• Loss % = LOSS/(CP)×100
• SP = (100-loss %)/100×C P
• CP = 100/(100-loss %)×S P

Profit and Loss Based on Cost Price

To find the percent gain or loss, divide the amount gained or lost by the cost and multiply it by 100. 

Example: A toy that cost 80 rupees is sold at a profit of 20 rupees. Find the percent or rate of profit.

Answer:

Gain/cost × 100 = % profit.

20/80 × 100 = 25%. - Answer

To find the loss and the selling price when the cost and the percent loss are given, multiply the cost by the percent and subtract the product from the cost.

Example: A damaged chair that cost Rs.110 was sold at a loss of 10%. Find the loss and the selling price.

Answer:

Cost x percent loss = loss.

110 x 1/10 = 11, loss.

Cost - loss = selling price.

110 - 11 = 99, selling price.

Profit and Loss Based on Selling Price

To find the profit and the cost when the selling price and the percent profit are given, multiply the selling price by the percent profit and subtract the result from the selling price.

Example: A toy is sold for Rs. 6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit.

Answer :

Selling price x % profit = profit.

Selling price = profit + cost.

6.00 x .25 = 1.50, profit.

6.00 - 1.50 = 4.50, cost.

To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price.

Example: At a sale, neckties selling at Rs. 50.00 are sold at a loss of 60% of the selling price. What are the loss and the original cost?

Selling price x % loss = loss.

Selling price + loss = cost.

50.00 x .60 = 30.00, loss.

50.00 - 30.00 = 20.00, cost.

To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum.

Example: Socks that cost 7.00 per pair were sold at a loss of 25% of the selling price. What was the selling price?

Answer: Cost / (100% + % loss) = selling price.

7.00 / 1.25 = 5.60, selling price.

To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss.

Note: This rule should be compared with the one under Profit and Loss Based on Cost. The two rules are exactly similar except that in one case 100% represents cost while in the other case 100% represents the selling price.

Example: A kind of tape is selling at a profit of 12% of the selling price, equal to 18 per yard. What is the selling price of the tape?

Answer: Profit / % profit = selling price.

18 /.12 = 1.50 selling price.

To find the percent profit or loss, divide the amount gained or lost by the selling price.

Example: A candy bar sells for 1.30 at a profit of 65. What percent of the profit on selling price does this represent?

Answer: Gain / selling price = % profit.

65 / 1.30 = .5 or 50% profit.

Mark-up Price

Generally, the SP is less than the marked price (MP) the difference MP – SP is known as the discount, D.

Discount = M P – S P

Discount %, D% = (Discount) / (MP) ×100

To reduce percent loss on the cost to percent loss on selling price, divide percent loss on the cost by 100% minus percent loss on cost.

 Example: 20% loss on cost is what percent loss on selling price?

Answer:

% loss on cost / (100% - % loss on cost) = % loss on selling price.

0.20 / 80 = .0025 or 25% loss on selling price

To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.

Example: 20% loss of selling price is what percent loss on cost?

Answer:

% loss on selling price / (100% + % loss on selling price) = % loss on cost.

.20 / 1.20 = .16666 or .16.67% loss on cost.

To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up.

Example: A coat marked up 60% carries what percent of the profit on selling price?

Answer : % profit on cost / ( 100% + % profit on cost ) = % profit on selling price.

.60 / 1.60 = .375 or 37.5% on selling price.