**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.

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**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

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**Profit Percentage**

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

Profit% = (Profit * 100)/CP

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**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.

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**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

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**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) %

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**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

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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

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**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

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**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