The profit and loss formula is a mathematical formula that is used to determine the market price of a commodity and to assess how lucrative a firm is.
There is a cost price and a selling price for every item.
We can compute the profit or loss made for a given product based on the values of these prices.
Cost price, fixed, variable, and semi-variable cost, selling price, marked price, list price, margin, and so on are all significant words discussed here.

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**Basic Profit and Loss Concepts**

Let's study profit and loss in math. In terms of cost price and selling price, it is properly stated.

**1 .Profit(P) **

is the profit earned when a product is sold for more than its cost price.

**2 .
Loss(L)**

A loss is the amount a seller loses after selling a product for less than its cost price.

**3 .Price of the product (CP)**

A cost price is the amount paid for a product or commodity at the time of purchase. Also abbreviated as CP. This cost price is further broken down into two categories:

**4.
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Fixed Cost:

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A fixed cost is one that remains constant regardless of the conditions.

Cost is variable and depends on the quantity of units ordered.

**5.
Price of Sale (SP)**

The Selling Price refers to the price at which a thing is sold. SP is the most common abbreviation. Also referred to as a selling price.

**6 .Formula for a Marked Price (MP)**

This is a term used by retailers to offer clients a discount in such a way that,

Discount = Selling Price – Marked Price, And Discount Percentage = (Discount/Marked price) x 100

**Formulas for Profit and Loss**

Let's look for the profit and loss formulas now.

The profit or gain is calculated by subtracting the selling price from the cost price.

The cost price minus the selling price is the loss.

Selling price – Cost Price = Profit or Gain

Cost Price – Selling Price = Loss

The profit and loss proportion is calculated using the following formula:

(Loss / Cost price) × 100 = Loss %

(Profit /Cost Price) x 100 = Profit %

** Questions and Answers **

**Question 1**

A merchant offers 8% discount on all his goods and still makes a profit of 15%. If an item is marked rs 250, then its cost price is

Option 1: 230

Option 2: 187

Option 3: 180

Option 4: 200

**Answer: **4: 200

**Explanation:**

**Question 2:**

If in a sale, the discount given on a saree is equal to one-fourth the marked price and the loss due to this discount is 15%, then the ratio of the cost price to the selling price is :

Option 1: 10:17

Option 2: 20:17

Option 3: 3:4

Option 4: 4:3

**Answer: **2: 20:17

**Explanation:**

**Question 3:**

In a 15% discount sale, the cost of a book is 2,150 What was the original price of the book? (Correct to two decimal places)

Option 1: 1527.00

Option 2: 2500.00

Option 3: 2529.41

Option 4: 2250.50

**Answer: **3: 2529.41

**Explanation:**

original price

original price = 43000/17=2529.41

**Question 4:**

The list price of an electric fan is rs 300. If two successive discounts of 15% and 10% are allowed, its selling price would be

Option 1: 227.50

Option 2: 225

Option 3: 230

Option 4: 229.50

**Answer: **4: 229.50

**Explanation:**

**Question 5:**

If in a business. Alok gains 75% more profit than Akash, then by what percentage profit of Akash is less than the profit of Alok?

Option 1: 42.85%

Option 2: 30.8%

Option 3: 12.63%

Option 4: 25%

**Answer:** 1: 42.85%

**Explanation:**

Let the profit of Alok be Rs. 100. then profit of Akash is ` 175. Required Profit percentage

175-100/175 X 100 = 42.85%

**Question 6:**

A chair marked at Rs 350 is available at successive discounts of 25% and 10%. The selling price of the chair is

Option1: 240.25 Rs

Option 2: 242.25 Rs

Option3: 236.25Rs

Option 4: 230.25 Rs

**Answer:** 3: 236.25Rs

**Explanation:**

Effective Discount Of Two Successive Discount = picture

**Question 7:**

The selling price and cost price of an article differs by 480. What is the selling price in case the profit percentage is 25% ?

Option 1: 2400

Option 2: 2880

Option 3: 2600

Option 4: 2800

**Answer:** 1: 2400

**Explanation:**

SP-CP=480 1.25x-x=480 ⇒0.25x = 480

X = 1920

So selling price SP = 1920 + 480 = 2400

**Question 8:**

If cost of 15 eggs be 75 rupees, then find out the cost of 5 dozen eggs.

Option 1: 300

Option 2: 400

Option 3: 500

Option 4: 600

Answer: 1: 300

Explanation:

Cost of 15 eggs = 75 rupees

Cost of 1 egg = 75/15 = 5 rupees, Cost Of Dozens,i.e.5x12=60x5=300

**Question 9:**

A stationer buys diaries at 75 rupees per dozen and sells them at 15 rupees per piece. What is the profit?

Option 1: 75

Option 2: 100

Option 3: 105

Option 4: 110

**Answer:** 3: 105

**Explanation:**

Each dozen carries cost 75 rupees and are sold for 12x15=180rupees

profit = SP-CP

profit = 180-75 = 105 rupees

**Question 10:**

A man bought 18 oranges for a rupee and sold them at 12 oranges for a rupee. what is the profit percentage ?

Option 1: 40%

Option 2: 50%

Option 3: 25%

Option 4: 30%

**Answer: **2: 50%

**Explanation:**

CP = 100/18 = 5.55 paisa

SP = 100/12 = 8.33 paisa

∴ Profit = (8.33-5.55)/5.55 x 100 = 50 %

**Question 11:**

On selling an article for Rs. 240, a trader loses 4%. In order to gain 10 % he must sell that article for

Option 1: Rs. 275

Option 2: Rs 340

Option 3: Rs 320

Option 4: Rs 240

**Answer: **1: Rs.
275

**Explanation:**

Let the CP be Rs.x,then SP be0.96x ∴ 0.96 x = 240

⇒x=250

Now the new SP=250X1.1=275

**Question 12:**

By selling 12 apples for a rupee, a man loses 20%. How many for a rupee should he sell to gain 20%

Option 1: 8

Option 2: 10

Option 3: 15

Option 4: 16

**Answer:** 1: 8

**Explanation:**

SP = 100/12 paise Let'sCP=x

SP = 0.8x = 100/12

∴ x = 10/(0.8x12) paise Therefore, CP = 100/9.6 paise

Thus the new SP (with 20% profit) = 100/9.6 X 1.2 = 100/8 paise

Hence, 8 apples can be purchased for Rs.1 to gain 20%

**Question 13:**

By selling a pen for Rs. 15, a man loses one sixteenth of what it costs him. The cost price of thepenis?

Option 1: 16

Option 2: 18

Option 3: 20

Option 4: 21

**Answer:** 1: 16

**Explanation:**

Let the C.P. be Rs. x. Then, x–15=x/16

⇒x–x/16=15

⇒15x/16=15

⇒x=16

∴C.P.=Rs.16.

**Question 14:**

By selling an article Michael earned a profit equal to one-fourth of the price he bought it. If he sold it for Rs. 375, what was the cost price ?

Option 1: 281.75

Option 2: 300

Option 3: 312.50

Option 4: 350

**Answer:** 2: 300

**Explanation:**

S.P. = C.P. + C.P./4= 5 C.P./4 ∴5C.P./4 = 375

⇒ C.P. = Rs. (375×4/5)= Rs. 300.

**Question 15 :**

10% loss on selling price is what percent loss on the cost price ?

Option 1: 9 1/ 11 %

Option 2: 9 2/11 %

Option 3: 10%

Option 4: 11%

**Answer:** 1: 9 1/11 %

**Explanation:**

Let S.P. = Rs. 100

Then, Loss = Rs. 10, C.P.=(100+10)=Rs.110

∴ Loss % =(10×100/110)%= %.

**Question 16:**

A trader mixes three varieties of groundnuts costing Rs. 50, 20 and Rs. 30 per kg in the ratio 2 : 4 : 3 in terms of weight, and sells the mixture at Rs. 33 per kg. What percentage of profit does he make ?

Option 1: 8%

Option 2: 9%

Option 3: 10%

Option 4: None of these

**Answer:** 3: 10%

**Explanation:**

Suppose he bought 2kg,4kg and 3kg of the three varieties.

C.P.of9kg=Rs.(2×50+4×20+3×30) = Rs. 270 S.P.of9kg=Rs.(9×33)=Rs.297

∴ Profit % = (27×100/270)% = 10%

.

**Question 17:**

A man buys 2 dozen bananas at Rs. 16 per dozen. Aer selling 18 bananas at the rate of Rs. 12 per dozen, the shopkeeper reduced the rate to Rs. 4 per dozen. The percent loss is ?

Option 1: 25.2

Option 2: 32.4

Option 3: 36.5

Option 4: 37.5

**Answer:** 4: 37.5

**Explanation:**

C.P.=Rs.(16×2)=32 S.P.=Rs.(12×1.5+4×0.5) =Rs.(18+2)=Rs.20

∴ Loss % = (12×100/32)% = 37.5%.

**Question 18:**

Some articles were bought at 6 for Rs. 5 and sold at 5 for Rs. 6. Gain percent is?

Option 1: 30%

Option 2: 33 ⅓%

Option 3: 35%

Option 4: 44%

** Answer**: 4: 44%

**Explanation:**

Suppose, number of articles bought= L.C.M. of 6 and 5 = 30

C.P. of 30 articles= Rs.5×30/6= Rs. 25

S.P. of 30 articles= Rs.6×30/5 = Rs. 36

∴Gain %=11×100/25=44%

**Question 19**

A man bought apples at the rate of 8 for Rs. 34 and sold them at the rate of 12 for Rs. 57. How many apples should be sold to earn a net profit ofRs.45?

Option 1: 90

Option 2: 100

Option 3: 135

Option 4: 150

**Answer: **1: 90

**Explanation:**

C.P. of 1 apple = Rs. 34/8= Rs. 4.25

S.P. of 1 apple = Rs. 57/12= Rs. 4.75

Profit on each apple = Rs. 0.50.

∴ Number of apples required =45/0.50= 90.

If loss is 1/3 of S.P, the loss percentage is ?

**Question 20: **

If loss is 1/3 of S.P, the loss percentage is ?

Option 1: 16 ⅔ %

Option 2: 20%

Option 3: 25%

Option 4: 33 ⅓ %

**Answer:** 3: 25%

**Explanation:**

S.P. = Rs. x Then, Loss = Rs. X/3

C.P. = Rs. (X+x/3)= Rs. 4x/3

∴ Loss % =( x/3)/(4x/3) ×100 = 25%.

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### What is Profit ?

It is the profit earned when a product is sold for more than its cost price.## What is loss ?

## What is Price of the product (CP) ?

## What is Fixed Cost ?

A fixed cost is one that remains constant regardless of the conditions.

Cost is variable and depends on the quantity of units ordered.