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## Profit & Loss Shortcuts

**Formulas of Profit and Loss**

**1.**Profit = Selling Price (S.P) - Cost Price (CP), when SP > CP

**2.**Loss = Cost Price (C.P) - Selling Price (S.P), when SP < CP

**3.**Profit % = (Profit / CP) x 100

**4.**Loss % = (Loss / CP) x 100

**5.**S.P = ((100 + Profit%)/100) x CP

**6.**S.P = ((100 - Loss%)/100) x CP

**7**. C.P = (100 / (100 + Profit%)) x SP

**8.**CP = (100 / (100 - Loss%)) x SP

**9.**If C.Ps of two articles are the same and after selling them profit % on one is same as the loss % on the other, then there will be no loss or no gain.

**10.**If SPs of two articles are the same and the profit % on one is same as the loss % on the other, then there will be a loss which is in % = (%x%) / 100

**11**. Two successive discounts of X% and Y% are equivalent to a single discount % of (X+Y) - ((XxY)/100)

**12.**Marked Price x Product of the balances of the discounts = Selling price to the seller or Cost price to the buyer.

**13.**Discount = Rebate = Concession = Reduction = Off [all are same]

**14.**

**Different names of marked price**: Label price, Labelled price, Printed price, Tag price, Announced price, Written price, Market price, List price, Original price etc.

**15.**Profit % after giving X% discount on the price which is Y% above the C.P = - X

**16.**The % of the C.P at which the labelled price be marked to get P% profit after giving d% discount = (100+P)/X1

**17.**The % above which the CP be marked to get P% profit after giving d% of discount = ((100+P)/X1) - 100

**18.**If one sells the goods at cost price, but gives X grams instead of 1 KG, where X <1kg complete="" nbsp="">

Gain % = (M/C) x 100,

**19.**The price per unit after the change in the price = (%/100) x (Amount/Change)

**20.**The price per unit before the change in the price = ((%/100+or-%)) x (Amount /Change)

### Profit & Loss : Examples and Practice Problems

__Model 1__

An article is bought for Rs. 600 and sold for Rs. 750. Find the gain % ? 20 25 27.5 30 None of these

Solution :

Practice Problems on Model 1 An article is bought for Rs. 16000 and sold for Rs. 1760. Find the gain % 20 15 10 12 None of these An article is bought for Rs. 2600 and sold for Rs. 3120. Find the gain % 20 25 15 10 None of these An article is bought for Rs. 18,600 and sold for Rs. 18,972. Find the gain % 1 1.5 2 3 None of these

__:__

**Model 2**An article is bought for Rs. 450 and sold for Rs. 400. What is the loss % ? 11 1/9 10 9 1/11 8 None of these

**Solution**:

Practice Problems on Model 2 An article is bought for Rs. 45000 and sold for Rs. 4250. What is the loss % ? 11 1/9 10 5 5/9 6 None of these An article is bought for Rs. 1760 and sold for Rs. 1650. What is the loss % ? 8 1/3 12 12 1/2 6 1/4 None of these

__:__

**Model 3**A man bought an article for Rs. 640 and sold at a profit of 15%. Find the selling price ? Rs. 673 Rs. 678 Rs. 736 Rs. 784 None of these

Solution :

__Method 1__:

__Method 2__:

**Practice Problems on Model 3**A man bought an article for Rs. 640 and sold at a loss of 15%. Find the selling price ? Rs. 454 Rs. 545 Rs. 554 Rs. 544 None of these A man bought an article for Rs. 24680 and sold at a loss of 22.5%. Find the selling price ? Rs. 5553 Rs. 16780 Rs. 19127 Rs. 18227 None of these

__:__

**Model 4**A plot is bought for Rs. 28,00,000 and sold at a profit of 14 2/7%. Find the selling price in lakhs of Rs. 30 31.5 32.25 36 None of these

Solution :

**(Total / Denominator) x CP = SP**

Practice Problems on Model 4 A plot is bought for Rs. 28,00,000 and sold at a profit of 10%. Find the selling price in lakhs of Rs. 29 30.4 31.2 30.8 None of these A plot is bought for Rs. 28,60,000 and sold at a profit of 19%. Find the selling price in lakhs of Rs. Rs. 5,43,400 Rs. 34,03,400 Rs. 32,25,560 Rs. 36,20,800 None of these A plot is bought for Rs. 28,80,000 and sold at a loss of 8 1/3 %. Find the selling price. Rs. 26,24,000 Rs. 27,20,000 Rs. 26,40,000 Rs. 24,60,000 None of these

__:__

**Model 5**A man sold a box for Rs. 450 at a gain of 25%. Find the cost price ? Rs. 400 Rs. 425 Rs. 350 Rs. 360 None of these

Solution :

Practice Problems on Model 5 A man sold a box for Rs. 585 at a loss of 2.5%. Find the cost price. Rs. 596 Rs. 600 Rs. 605 Rs. 620 None of these A man sold a box for Rs. 960 at a gain of 20%. Find the cost price Rs. 880 Rs. 840 Rs. 780 Rs. 800 None of these A man sold a box for Rs. 1221 at gain of 11%. Find the cost price ? Rs. 1000 Rs. 1010 Rs. 1100 Rs. 1110 None of these

**:**

__Model 6__An article is sold for Rs. 375 at a loss of 6 1/4 %. Find the cost price ? Rs. 400 Rs. 380 Rs. 381.25 Rs. 360 None of these

Solution :

**Note**: for Loss we should write difference / denominator]

__Practice problems on Model 6__:

An article is sold for Rs. 5250 at a loss of 9 1/11 %. Find the cost price ? Rs. 5500 Rs. 5575 Rs. 5650 Rs. 5785 None of these An article is sold for Rs. 1012 at a loss of 4 1/6%. Find the cost price. R.s 1056 Rs. 1064 Rs. 1100 Rs. 1122 None of these An article is sold for Rs. 3225 at a gain of 7 1/2%. Find the cost price ? Rs. 2800 Rs. 2960 Rs. 3000 Rs. 3050 None of these

__Model 7__:

A bought a ring and sold it to B at 10% profit and B sold it to C at a loss of 20%. If C paid Rs. 22,000, for how many Rs. did A buy it ? Rs. 20,000 Rs. 22,500 Rs. 25,000 Rs. 27,750 None of these

Solution :

__:__

**Practice Problems on Model 7**A bought a ring and sold it to B at 10% loss and B sold it to C at a loss of 10%. If C paid Rs. 29,160, for how many Rs. didi A buy it ? Rs. 30,000 Rs. 32,500 Rs. 35,000 Rs. 37,750 None of these A bought a ring and sold it to B at 12% profit and B sold it to C at a loss of 2%. If C paid Rs. 21,952 for how many Rs. did A buy it ? Rs. 20,000 Rs. 20,500 Rs. 21,000 Rs. 19,600 None of these A bought a ring and sold it to B at 10% profit and B sold it to C at a profit of 7%. If C paid Rs. 1,31,824, for how many Rs. did A buy it ? Rs. 1,00,000 Rs. 1,12,000 Rs. 1,20,000 Rs. 1,16,000 None of these

__:__

**Model 8**The cost price of an object is numerically equal to its profit % and its selling price is Rs. 56. What is its cost price ? Rs. 20 Rs. 36 Rs. 40 Rs. 50 None of these

Solution :

*x*,

*x*%

*x*) / 100) x

*x*= 56

**Answer option 1**:

*x*= 20 => (120/100) x 20 not equals to 56

**Answer option 2**:

*x*= 36 => (136/100) x 36 not equals to 56

**Answer option 3**:

*x*= 40 => (140/100) x 40 = 56

__:__

**Practice Problems on Model 8**The cost price of an object is numerically equal to its profit % and its selling price is Rs. 75. What is it's cost price ? Rs. 20 RS. 36 Rs. 40 Rs. 50 None of these The cost price of an object is numerically equal to its profit % and its selling price is Rs. 31.25. What is its cost price ? Rs. 15 Rs. 25 Rs.28 Rs. 30 None of these T he cost price of an object is numerically equal to its profit % and its selling price is Rs. 77.36. What is cost price ? Rs. 56 Rs. 54 Rs. 66 Rs. 64 None of these

__:__

**Model 9**The profit obtained by selling an article for Rs. 56 is same as the loss obtained by selling it for Rs. 42. What is its CP ? Rs. 49 Rs. 50 Rs. 48 RS. 46 None of these

Solution :

**:**

__Practice Problems on Model 9__**The profit obtained by selling an article for Rs. 38 is same as the loss obtained by selling it for Rs. 22. What is its CP ?**- Rs. 30
- Rs. 32
- RS. 25
- Rs. 28
- None of these
**The profit obtained by selling an article for Rs. 256 is same as the loss obtained by selling it for Rs. 142. What is CP ?**- Rs. 149
- Rs. 199
- Rs. 201
- Rs. 211
- None of these
**The profit obtained by selling an article for Rs. 54 is same as the loss obtained by selling it for Rs. 40. What is the CP ?**- Rs. 49
- Rs. 50
- Rs. 48
- Rs. 46
- None of these

__:__

**Model 10****The profit obtained by selling an article for Rs. 48 is twice the loss obtained by selling it for Rs. 30. What is its CP ?**- Rs. 42
- Rs. 40
- Rs. 38
- Rs. 36
- None of these

**Solution :**

CP = 30+Loss = 48-Profit

=> Loss + Profit = 48-30 = 18

=> L + 2L = 18 => L = 6

CP = 30+6 = 36

CP = 30+6 = 36

__:__

**Practice Problems on Model 10****The profit obtained by selling an article for Rs. 46 is thrice the loss obtained by selling it for Rs. 30. What is its CP ?**- Rs. 42
- Rs. 40
- Rs. 38
- Rs. 36
- None of these
**The profit obtained by selling an article for Rs. 48 is half of the loss obtained by selling it for Rs. 30. What is its CP ?**- Rs. 42
- Rs. 40
- Rs. 38
- Rs. 36
- None of these
**The profit obtained by selling an article for Rs. 48 is 1/5th of the loss obtained by selling it for Rs. 30. What is it's CP ?**- Rs. 42
- Rs. 40
- Rs. 38
- Rs. 36
- None of these

**:**

__Model 11__**A man sold 2 articles for Rs. 495 each. On one he gains 10% and on the other he losses 10%. Find the total loss ?**- Rs. 4.95
- Rs. 5
- Rs. 9.90
- Rs. 10
- None of these

**Solution :**

2 articles selling prices same, then Loss % = (% x %) / 100

=> (10 x 10) / 100 = 1% loss

Cost Price - Loss = Selling Price

That means, if he buys the items for Rs. 100

Then, the Selling Price will be 100 - 1 =

**99**
But here the selling price = 2 * 495 =

**990**
So the total loss will be Rs. 10

__:__

**Practice Problems on Model 11****A man sold 2 articles for Rs. 240 each. On one he gains 20% and on the other he losses 20%. Find the total loss ?**- Rs. 9.60
- Rs. 20
- Rs. 19.20
- Rs. 10
- None of these
**A man sold 2 articles for Rs. 495 each. On one he gains 10% and on the other he losses 10%. Find the sum of their cost prices ?**- Rs. 500
- Rs. 990
- Rs. 1000
- Rs. 960
- None of these
**A man sold 2 articles for Rs. 1920 each. On one he gains 20% and on the other he losses 20%. Find the sum of their cost prices ?**- Rs. 4000
- Rs. 2000
- Rs. 3600
- Rs. 1800
- None of these

**:**

__Model 12__**The cost price of 3 articles is same as the selling price of 2 articles. What is the loss or gain % ?**- 50% loss
- 50% gain
- 25% loss
- 25% gain
- None of these

**Solution :**

Let the Cost Price per article be Rs.

*x*

and Selling Price per article b Rs.

*y*

CP of 3 articles = SP of 2 articles

=> 3

*x*= 2*y*

*=> x*:

*y*= 2 : 3

*=> x*= 2K &

*y*= 3 K [where K is some constant number]

Profit = SP - CP

= 3K - 2K = K

Profit % = (Profit / CP) x 100 = (K/2K) x 100 = 50%

__:__

**Practice Problems on Model 12****The cost price of 2 articles is same as the selling price of 3 articles. What is the loss or gain % ?**- 50% loss
- 33 1/3% gain'
- 25% loss
- 33 1/3% loss
- None of these
**The cost price of 13 articles is same as the selling price of 12 articles. What is the loss or gain % ?**- 8 1/3 % gain
- 12 2/3 % gain
- 8 1/3% loss
- 12 2/3 % loss
- None of these
**The cost price of a dozen articles is same as the selling price of a score articles. What is the loss or gain % ?**- 50% loss
- 50% gain
- 40% loss
- 40% gain
- None of these

**[Note :**

*Dozen - 12*,*Score = 20*]**Work with these models and solve the given practice problems. Meanwhile I will post more methods with shortcuts. After completing these problems just REFRESH this page to get more methods**

**. All the Best :)**

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