Profit, Loss and Discount over Cost Price and Selling Price – Formulas and comprehensive concepts are widely used in school mathematics and competitive exams (Bank PO/Clerk, CTET, SUPER TET, RRB, UPP, SSC, UPSSSC, UPSC). It is most important for business understanding, business hopes.
Profit and loss are higher order thinking chapter for all students and aspirant. Approx all the competitive exams carry at least two question in their prelims exams, directly or through reasoning. After analysing aspect ratio of all competitive exams, Profit and Loss chapter are most important for very aspirant.
In those days, many shopping complex or online shopping sites are offer complex discount during festival. In between this many of you get confused and get loss after purchasing a products.
Let’s explore each comprehensive guide regarding Profit and Loss which are provided by our subject experts.
Table of Contents
What are Profit and Loss?
When a seller/vendor sells a product at higher price than the cost price then, difference between Selling price and Cost price is known as Profit(P) or Gain(G). This means, In case of Profit, Selling price will be always greater than Cost Price.
Examples: A book seller/vendor bought a pen at ₹5 and sell at ₹7. His profit is ₹2.
When a seller/vendor sells a product at lower price than cost price then, difference between Selling price and Cost price is known as Loss(L). This means, In case of Loss, Cost Price will be always greater than Selling Price.
Examples: A book seller/vendor bought a pen at ₹5 and sell at ₹4. His loss is ₹1.
Interactive Profit and Loss Calculator
Use the sliders below to adjust the selling price and cost price. The profit or loss will be calculated along with a visual graph. Observe
Profit/Loss: ₹0
Calculation: Selling Price – Cost Price = Profit/Loss
Important Term Used in Profit And Loss.
Cost Price (CP): The price at which a seller/vendor purchases a product or original price of product is known as Cost Price (CP).
Selling Price(SP): The price at which a seller/vendor sell a product or amount pay by customer/shopper/buyer to seller/vendor is known as Selling Price(SP).
Successive Selling: When a product is sold multiple time from buyer to other at some profit or loss. Those price are known as Successive Selling. Example: A sold a car to B at profit and B sold same car to C at more profit.
Marked Price (MP): The Price which are labelled/written by seller/vendor on product to give offer or discount to their customers.
Discount(D): The amounts which are offer/reduced by seller/vendor to customer during purchasing a product.
Successive Discount: When a seller/vendor offer two discounts(discount pe discount) on same products then, discounts are known as Successive Discount.
Sales Tax: When customers pay extra amount while purchasing a product other than selling price. Sales tax is calculated over the selling price of a product.
Profit and Loss Formulas with Tricks
Let us learn all formulas with fast tricks which are use to solve maths questions problem based on profit and loss within seconds. First conditions, Remember all the formulas clearly. Second, try to solve too many problems related to it.
- Cost Price = CP
- Selling Price = SP
- Marked Price = MP
- Discount = D
| What to Find? | Given in Questions | Formulas |
| Profit | SP and CP | = SP - CP |
| SP | Profit and CP | = CP + Profit |
| CP | Profit and SP | = SP - Profit |
| Loss | SP and CP | = CP - SP |
| SP | Loss and CP | = CP - Loss |
| CP | SP and Loss | = SP + Loss |
| Loss% | Loss and CP | \(\left( \frac{loss }{CP} \times100\right) \%\) |
| Profit% | Profit and CP | \(\left( \frac{Profit }{CP} \times100\right) \%\) |
| SP | Profit% and CP | \(\left( \frac{100+Profit \%}{100} \right) \times CP\) |
| CP | Profit% and SP | \(\left( \frac{100}{100+profit\%} \right) \times SP\) |
| SP | Loss% and CP | \(\left( \frac{100-Loss\%}{100} \right) \times CP\) |
| CP | Loss% and SP | \(\left( \frac{100}{100-Loss\%} \right) \times SP\) |
| Discount | MP and SP | = MP - SP |
| SP | Discount and MP | = MP - Discount |
| MP | Discount and SP | = SP + Discount |
| Discount% | Discount and CP | \(\left( \frac{Discount}{CP}\right) \times100\) |
Q. If the cost price of 6 pencils is equal to the the selling price of 5 pencils. find the gain per cent.
Solutions: Let the cost price of each pencil be ₹1. Then,
CP of 5 pencils = ₹5.
Gain = SP - CP = ₹(6 - 5) = ₹1
Gain%\(=\left( \frac{Gain }{CP}\times100 \right)\% = \left( \frac{1 }{5}\times100\right)\% = 20\% \)
Q. If the cost price of 15 pens is equal to the selling price of 20 pens. Find the loss per cent.
Solution: Let the CP of each pen be ₹1.
CP of 15 pens = ₹ 15
SP of 15 pens = CP of 15 pens = ₹15.
Thus, CP = ₹ 20 and SP = ₹15
Loss = CP - SP = ₹(20 - 15) = ₹5
Loss%\(=\left( \frac{Loss }{CP}\times100 \right)\% = \left( \frac{5 }{20}\times100\right)\% = 25\% \)
Q. A man sold two radios at ₹4800 each. On one he gains 20% and on the other he loss 20%. Find the gain or loss per cent in the whole transactions.
Solution: First radio:
SP =₹4800, gain = 20%
∴ CP \(=\left( \frac{100}{100+gain\%} \right) \times SP\)
\(=\left( \frac{100}{100+20} \right) \times 4800\) = ₹\(\left( \frac{100}{120} \times 4800 \right)\) = ₹4000.
Second radio:
SP = ₹ 4800, Loss = 20%
∴ CP\(=\left( \frac{100}{100+loss\%} \right) \times SP\)
= ₹\(\left( \frac{100}{100 - 20} \right) \times 4800\) = ₹\(\left( \frac{100}{80} \times 4800 \right)\) = ₹6000.
Total CP = ₹(4000 + 6000) = ₹10,000.
Total SP = ₹(4800 + 4800) = ₹9600. Here, SP > CP. Then
Loss% \(=\left( \frac{Loss }{CP}\times100 \right)\% = \left( \frac{400 }{10000}\times100\right)\% = 4\% \)
Q. If the profit made on a packet of tea is ₹4 and the cost price of the packet is ₹20, then how much is the profit percentage?
Solution: we have, C.P = ₹20 and Profit = ₹4.
∴Profit% \(=\left( \frac{Gain }{CP}\times100 \right)\% = \left( \frac{4}{20}\times100\right)\% = 20\% \)
Q. Subramanian bought 100 eggs for ₹50. Out of these, 4 eggs were found to be broken. He sold the remaining eggs at ₹8.50 per dozen. Find his gain or loss percent.
Solution: We have,
C.P of 100 eggs = ₹50.
It is given that 4 eggs were found to be broken.
∴ The number of the remaining eggs which were sold in the market = 100 - 4 = 96.
It is given that remaining eggs were sold at the rate of ₹ 8.50 per dozen.
∴ S.P of 12 eggs = ₹8.50 ⇒ S.P of 1 egg\(=\left( \frac{₹8.50 }{12}\right)\)
∴ S.P of 96 eggs\(=\left( \frac{₹8.50 }{12}\times96\right)\)=₹68
Clearly, S.P > C.P. so, there is gain given by gain = S.P - C.P = ₹68 - ₹50 = ₹18.
∴ Gain% \(=\left( \frac{Gain }{CP}\times100 \right)\% = \left( \frac{18 }{50}\times100\right)\% = 36\% \)
Q. A grocer buys eggs at 10 for ₹8 and sells at 8 for ₹10. Find his gain or loss percentage.
Solution: we have, LCM of 10 and 8 = 40. so,
Let the number of eggs bought be 40.
Now,
C.P of 10 eggs = ₹8.
∴ C.P of 40 eggs \(=\left( \frac{₹8}{10}\times40\right)\) = ₹32
Again, S.P of 8 eggs = ₹10
∴ S.P of 40 eggs \(=\left( \frac{₹10}{8}\times40\right)\) = ₹50
Clearly, SP > CP. so, gain = ₹50 - ₹32 = ₹18.
∴ Gain% \(=\left( \frac{Gain }{CP}\times100 \right)\% = \left( \frac{18 }{32}\times100\right)\% = \frac{225}{4}\%\)
Q. The selling price of 10 articles is the same as the cost price of 11 articles, find gain percent.
Solution: Let the cost price of each article be ₹x
we have,
S.P of the 10 article = C.P of 11 articles = ₹11x.
CP of 10 articles = 10x.
∴ Gain on the purchase of articles = ₹11x - ₹10x = ₹x
Hence, Gain%\(=\left( \frac{Gain }{CP}\times100 \right)\% = \left( \frac{x}{10x}\times100\right)\% = 10\%\)
Q. Neeru bought 1600 bananas at ₹3.75 a dozen. She sold 900 of them at 2 for ₹1 and the remaining at 5 for ₹2. Find her gain or loss percentage.
Solution: we have,
Cost of dozen of bananas = ₹3.75
∴ Cost of 1600 bananas\(=\left( \frac{₹3.75 }{12}\times1600\right)\) = ₹500
Thus, C.P of 1600 bananas = ₹500
Now, Selling price of 900 bananas at the rate of 2 for ₹1\(=\left( \frac{₹900}{2}\right)\) = ₹450.
Selling price of the remaining, 1600 - 900 = 700 bananas at the rate of 5 for the ₹2. then, \(=\left( \frac{₹2}{5}\times700\right)\) = ₹280.
∴ S.P of 1600 bananas = ₹(450 + 280) = ₹730.
Since, S.P > C.P then, gain = S.P - C.P = ₹(730 - 500) = ₹230.
Hence, Gain%\(=\left( \frac{Gain }{CP}\times100 \right)\% = \left( \frac{230}{500}\times100\right)\% = 46\%\)
Q. If a pen cost ₹50 after 10% discount, then what is the actual price or marked price of the pen?
Solution: we know that, SP = MP - D
⇒SP = MP – \(\left( \frac{Discount}{CP}\right) \times 100\)
⇒SP = MP x \(\left(\frac{100-D%}{100}\right)\)
Putting the SP = ₹50, Discount = 10% values in formula
⇒SP = MP x\(\left( \frac{100-10}{100} \right)\)
⇒MP x \(\left( \frac{90}{100}\right)\) = ₹50
⇒MP = \(\left( \frac{50 x 100}{90} \right)\)
⇒MP = ₹55.55
Q. Marked price of a book is ₹1000 and it is sold at ₹800. Find the discount percentage.
Solution: we know that, Discount = (MP – SP) ⇒ ₹(1000 – 800) = ₹200
Discount%\(=\left( \frac{Discount}{CP}\right) \times 100\) ⇒ \(=\left( \frac{200}{1000}\right) \times 100\)= 20%.
Q. Marked price of a dairy product is Rs 240 and allow 25% discount on it. Find the selling price of product.
Solution: Discount = SP × 25% ⇒ \(240 \times \frac{25}{100}\) = ₹60
SP = MP – Discount = ₹(240 – 60) = ₹180.
Alternate Method: SP = ₹(100 – D %) × \(\frac{MP}{100} \) ⇒ (100 – 25) × \(\frac{240}{100}\) = ₹180.
Q. A Cap is sold after providing two successive discounts of 20%. If the marked price of a Cap is ₹200 then find the selling price of Cap.
Solution: First Discount = 200 × \(\frac{20}{100}\) = ₹40
⇒SP after First discount = ₹(200 – 40) = ₹160.
⇒Second Discount = 160 ×\(\frac{20}{100}\) = ₹32
⇒SP after Second discount = ₹(160 – 32) = ₹128
Alternate Method: Effective discount = (20 + 20) – \(\frac{20 × 20}{100}\) = 36%
⇒Discount = 200 × \(\frac{36}{100}\) = ₹72
⇒SP = ₹(200 – 72) = ₹128
Q. A man gains 30% by selling an article for a certain price. If he sells it at double the current selling price, then what will be the profit percentage?
Solution: Let, the cost price of an article be ₹x , and given gain% = 30%
SP = \(=\left( \frac{100+Profit\%}{100} \right) \times CP\) ⇒ \(\left( \frac{100+30 \%}{100} \right) \times x\) = ₹1.3x
∴ SP = Rs. 1.3x
Acc to Q, if SP is double..
Now, new SP = ₹2.6x then, profit = new SP - CP ⇒ ₹(2.6x - x) = 1.6x
∴ Profit%\(=\left( \frac{Profit }{CP}\times 100 \right) \%\) ⇒ \(\left( \frac{1.6x}{x}\times 100 \right) \%\) = 160%
Q. A man sold 2 bikes at the same selling price. One at 20% loss and other at 20% profit. Find overall profit and loss percentage.
Solution: Let the SP of bike be 300x.
given loss% = 20%
We know that, CP\(=\left( \frac{100}{100-Loss\%} \right) \times SP\)
Then, CP for 1st bike = 250x
Similarly,
CP\(=\left( \frac{100}{100+profit\%} \right) \times SP\)
Then, CP of 2nd bike = 375x
Hence, Net CP = 625x and net SP = 600x then, loss = 4x.
∴ Net loss % = \(\left( \frac{25x}{625x} \right) \times 100\) = 4%
Q. 10 books costs ₹100 each. If half of the pencils are sold at 10% loss then find at what price remaining each pen should be sold for making no loss and no profit.
Solution: Total CP of 10 books = 10 × ₹100 = ₹1000
SP of 1 book = 100 – (100 × 10%) = ₹90
Hence, SP of 5 books = ₹450
Now, SP of remaining 5 books = ₹(1000 – 450) = ₹550
Hence, SP of 1 book = ₹110
∴ Profit% = \(\frac{110 – 100}{100} \) = 10%
Q. The average cost price of two articles P and Q is ₹1350. Article P sold at 10% profit and article Q sold at 20% profit. The total selling price of article P and Q is ₹3120. If article Q is sold at 40% Profit, then the selling price. (SBI PO 2023)
Solution: Total cost price of P and Q = ₹1350×2 = ₹2700.
Let cost price of article P = ₹x.
So, cost price of article Q = ₹(2700 -x).
Acc to Ques,
We know that, SP =\(\left( \frac{100+Profit \%}{100} \right) \times CP\)
⇒\(\left( \frac{100+10 \%}{100} \right) \times x\) + \(\left( \frac{100+20 \%}{100} \right) \times \left(2700 - x \right)\) = ₹3120
⇒1.1x + 3240 - 1.2x = ₹3120
⇒0.1x = ₹120
⇒x = ₹1200 cost price of P
Then, Cost Price of Q = ₹(2700 - 1200) = ₹1500
Required selling price of Q = ₹1500\(\times \left( \frac{100 + 40}{100} \right)\)= ₹2100.
Q. P and Q started a business by investing ₹15000 & ₹(15000+x) respectively. After four months, Q withdrew 40% of his initial investment. After a year, the total profit was ₹4700 and the profit share of Q was ₹22000. Find the value of 2x.
Solution: Profit ratio of P and Q respectively = \(\frac{15000 \times 12}{ \left(15000+x \right) \times 4 + \left[ \left(15000 + x \right) \times \frac{60}{100} \times 8 \right]}\)
= \(\frac{180000}{ \left(132000 + 8.8x \right)}\)
Acc to Ques,
\(\frac{180000}{ \left(132000 + 8.8x \right)} = \frac{47000 - 22000}{2200}\)
⇒0.8x = 2400
⇒x = ₹3000
so, 2x = ₹6000
What do you mean by Profit and Loss in Math?
If selling price of product is higher than cost price (SP > CP) in whole transaction is said to Profit. If cost price of product is higher than selling price (CP > SP) in whole transaction is said to Loss.
What is formula to find out CP if SP, loss and profit percentage are given?
If Selling price, Profit or loss percentage are given:
CP\(=\left( \frac{100}{100+profit\%} \right) \times SP\)
CP\(=\left( \frac{100}{100-Loss\%} \right) \times SP\)
What is formula to find out SP if CP, loss and profit percentage are given?
If Cost price, Profit or loss percentage are given:
SP\(=\left( \frac{100+Profit\%}{100} \right) \times CP\)
SP\(=\left( \frac{100-Loss\%}{100} \right) \times CP\)
What do you mean Selling price and Cost price?
The price at which product is sold by vender is selling price, and the price at which product is purchased by vendor is cost price.
What do you mean by Marked Price?
This price is set by retailer/vendor before offering the discount on a products is said to be Marked price.
It is known as Market Price.
Ratio and Proportion questions banks for class 7.
Mathac.com is providing basic concepts, aptitude questions on Ratio & Proportion for class 7 with...
SBI PO Math & Reasoning Case Based Study Questions with Solution PDF.
Are you looking for Math case-based study questions for SBI PO exams in 2025? If...
Profit and Loss-Formulas, Basic & Comprehensive Concepts with suitable examples.
Profit, Loss and Discount over Cost Price and Selling Price – Formulas and comprehensive concepts...
CBSE Class 10 Basic Maths Pre-Board Sample Paper 2025 With Solutions: Download PDF for Free
CBSE Class 10th Basic Mathematics Pre-Board papers 2025 with expert solution in pdf: it your...
CBSE Class 10 Math Success: Ultimate Guide with Tips and Strategies
CBSE Class 10 Mathematics Exam: Tips, Strategies, and Resources The CBSE Class 10 board exams...
Last-months Preparation tips for Math to score above 90% in CBSE 10th Board.
Are you searching on Google for a smart and effective last-minute preparation plan for your...