Profit, Loss and Discount

Following are the some important definitions related to profit and loss concepts. Understanding these is important before you get started with solving profit and loss problems.

Cost Price (CP)

The price at which items are bought is called the cost price.

Selling Price (SP)

The price at which items are sold is called the selling price.

Overhead Expenses

Sometimes when an article is purchased, some additional expenses are made after buying it. These expenses are added to the cost price (C.P.) of the article. These expenses are called overhead expenses. For example, when we buy an old item, we spend on its repairing, transportation, etc. These extra expenditures are overhead expenses.

Profit

When the selling price is more than the cost price, then the shopkeeper makes a profit which is equal to SP - CP.

Profit = SP - CP

Loss

When the selling price is less than the cost price, then the shopkeeper incurs a loss which is equal to CP - SP.

Loss = CP - SP

Profit Percentage

The value of profit, when expressed as a percentage of the cost price (CP), is called profit percentage.

Profit% = (Profit * 100)/CP

Loss Percentage

The value of loss, when expressed as a percentage of the cost price (CP), is called loss percentage.

Loss% = (Loss * 100)/CP

Note: Profit or loss percentage is always calculated as a percentage of cost price unless mentioned in the question.

Marked Price, Selling Price and Discount

Marked price (MP) is the price that is marked on the item or that is quoted in the price list. It is the price at which the item is quoted to be sold. However, the shopkeeper can decide to give discounts to the buyer and the actual selling price might be different from the marked price. Marked price is also called list price (LP). Given that there is no discount, the marked price is the same as the selling price.

Discount = MP - SP

Discount is always calculated on marked price. This can be expressed as

Discount% = (Discount * 100)/MP

Profit and Loss Shortcuts

Here is an important shortcut to solve profit and loss problems when it is based on successive discounts.

If the first discount is a% and the second discount is b%, then

Total discount = (a + b - ab / 100) %

Solved Examples on Profit, Loss and Discount

Example 1: A cow costing Rs 3500 is sold at Rs 2940. Find the loss per cent.

Solution: CP of cow = Rs 3500, SP of cow = Rs 2940

Loss = Rs (3500 – 2940) = Rs 560

We know that, Loss% = (Loss * 100)/CP

Loss% = (560 * 100)/3500 = 16%

Thus, the loss percentage is 16%.

Example 2: A shopkeeper purchased 150 eggs for Rs 400. 10 eggs were broken in

transportation and were thrown away. He sold the remaining eggs at Rs 3 per egg.

Find his gain or loss per cent.

Solution: Cost price = Rs 400

10 eggs were broken, so remaining eggs = 150 – 10 = 140

Selling price of 140 eggs = Rs 3 × 140 = Rs 420

Here, S.P. > C.P., there is a profit.

Profit = S.P. – C.P.

= Rs 420 – Rs 400 = Rs 20

Profit% = (Profit * 100)/CP

= (20 * 100)/400

= 5%

Hence, the shopkeeper gains 5%.

Example 3: If the selling price of 6 articles is equal to the cost price of 9 articles, then find the gain or loss per cent.

Solution: Let the cost price of each article be Rs 1.

Then CP of 6 articles = Rs 6

SP of 6 articles = CP of 9 articles = Rs 9

Gain = 9 – 6 = Rs 3

So, gain% = (3 × 100)/6 = 50%

Thus, the gain percentage is 50%.

Example 4: During a sale, a television set was sold for Rs 23,800. If the marked price of the television set was Rs 34,000, find the percentage discount.

Solution: Discount = Rs 34,000 – Rs 23,800

= Rs 10,200

Percentage discount = (10,200 × 100)/34,000 % = 30%

Thus, the discount on the television set is 30%.

Example 5: In a sari sale, a sari is sold for Rs 2990 after allowing 35% discount, what is the marked price?

Solution: Let the marked price be Rs 100.

Discount = Rs 35

Selling price (SP) = Rs (100 – 35) = Rs 65

If SP is Rs 65, then the marked price = Rs 100

If SP is Rs 1, then the marked price = Rs 100/65

If SP is Rs 2990, then the marked price = Rs (100 × 2990)/65 = Rs 4600

Hence, the marked price of the sari is Rs 4600.

Example 6: The marked price (MP) of a pair of trousers is Rs.1000. A shopkeeper offers 30% discount on this pair of trousers and then again offers a 20% discount on the new price. How much will you have to pay, finally?

Solution: As the successive discount is 30% and 20%,

Then, a = 30% and b = 20%
Total discount = [a + b – (ab)/100]%
Total discount = [ 30 + 20 – (30 × 20 )/100]% = (50 – 600/100)% = 44%
Discount = 44% of 1000 = [44/100] × 1000 = Rs.440
Selling price (SP) = marked price (MP) – discount = 1000 – 440 = Rs.560

Goods and Services Tax (GST)

Goods and services tax (GST) is an indirect tax levied on the supply of goods and services. This tax has replaced many indirect taxes that previously existed in India.

GST has removed the cascading effect on the sale of goods and services. The removal of cascading has directly impacted the cost of goods. Since tax on tax is eliminated, it resulted decrease in the cost of goods.

GST = Price of consumption × GST rate

Solved Examples on GST

Example 1: An electrician charges Rs 200 for a service excluding GST. If GST rate is 8%,

a. how much is the GST for the service provided?

b. how much does a customer have to pay for the service including GST?

Solution:

a. GST = Service charge × GST rate

= Rs 200 × 8%

= Rs 200 × 8/100 = Rs 16

Customer has to pay GST of Rs 16.

b. Total amount = Service charge + GST

= Rs 200 + Rs 16

= Rs 216

Thus, customer has to pay Rs 216 for the repairing service including GST.

Example 2: The marked price of a TV set is Rs 23,600 including GST. The GST rate is 18%.

a. Find its price before GST.

b. Find the amount of GST levied on it.

Solution:

a. Marked price = Price before GST × (100% + GST rate)

23,600 = Price before GST × (100% + 18%)

= Price before GST × 118%

Price before GST = 23,600 /118%

= (23,600 × 100) /118

= Rs 20,000

Thus, price before GST is Rs 20,000.

b. GST = Marked price – Price before GST

= Rs 23,600– Rs 20,000 = Rs 3,600

Profit, Loss and Discount