SBI Clerk 2018 Coaching Day 3 - Profit and Loss (Shortcuts & Practice Tests)

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Hello friends. Today we shall learn the shortcut techniques of Profit and Loss. Happy Reading :)

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 + Y + ((-X) (Y)) / 100

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

Where X1 = balance % of the discount => MP = ((100+P)/X1)% of CP

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

where X1 = balance % of the discount 

18. If one sells the goods at cost price, but gives X grams instead of 1 KG, where X <1kg complete="" nbsp="">
the Gain % = ((1000- X)/X) x 100   (or)
 
Gain % = (M/C) x 100,

where M = Weight retained by the Merchant and C  = Weight given to the Customer 

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 :

1.  An article is bought for Rs. 600 and sold for Rs. 750. Find the gain % ?
1. 20
2. 25
3. 27.5
4. 30
5. None of these 

Solution :

Cost Price (CP) = 600
Selling Price (SP) = 750

Gain % = (Gain/CP) x 100

=> (150/600) x 100 = 25%

Practice Problems on Model 1

1. An article is bought for Rs. 16000 and sold for Rs. 1760. Find the gain %
1. 20
2. 15
3. 10
4. 12
5. None of these 
2. An article is bought for Rs. 2600 and sold for Rs. 3120. Find the gain %
1. 20
2. 25
3. 15
4. 10
5. None of these 
3. An article is bought for Rs. 18,600 and sold for Rs. 18,972. Find the gain %
1. 1
2. 1.5
3. 2
4. 3
5. None of these 

Model 2 :

1. An article is bought for Rs. 450 and sold for Rs. 400. What is the loss % ?
1. 11 1/9
2. 10
3. 9 1/11
4. 8
5. None of these 

Solution :

CP = 450

SP = 400

Loss % = (Loss/CP) x 100 = (50/450) x 100 = 100/9 = 11 1/9

Practice Problems on Model 2

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

Model 3 :

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

Solution :

Method 1 :

We all know, 10% of 640 is 64

So, 5% of 640 will be 32

So 15% will be 64+32 = 96

Selling price = Original Price + 15% Price 

= 640 + 96  = 736

Method 2 :

15% = 15/100 = 3/20 Profit -> this means if we buy for Rs. 20, we sell it for 3 rupees profit. 

So, (23/20) x CP = SP

(23/20) x 640 =  736

Practice Problems on Model 3

1. A man bought an article for Rs. 640 and sold at a loss of 15%. Find the selling price ?
1. Rs. 454
2. Rs. 545
3. Rs. 554
4. Rs. 544
5. None of these 
2. A man bought an article for Rs. 24680 and sold at a loss of 22.5%. Find the selling price ?
1. Rs. 5553
2. Rs. 16780
3. Rs. 19127
4. Rs. 18227
5. None of these 

Model 4 :

1. 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. 
1. 30
2. 31.5
3. 32.25
4. 36
5. None of these 

Solution :

14 2/7% = 100 / (7x100) = 1/7%

Remember that (Total / Denominator) x CP = SP

=> 8/7 CP = SP

(8/7) x 28,00,000 = 32,00,000

Practice Problems on Model 4

1. A plot is bought for Rs. 28,00,000 and sold at a profit of 10%. Find the selling price in lakhs of Rs. 
1. 29
2. 30.4
3. 31.2
4. 30.8
5. None of these 
2. A plot is bought for Rs. 28,60,000 and sold at a profit of 19%. Find the selling price in lakhs of Rs. 
1. Rs. 5,43,400
2. Rs. 34,03,400
3. Rs. 32,25,560
4. Rs. 36,20,800
5. None of these 
3. A plot is bought for Rs. 28,80,000 and sold at a loss of 8 1/3 %. Find the selling price. 
1. Rs. 26,24,000
2. Rs. 27,20,000
3. Rs. 26,40,000
4. Rs. 24,60,000
5. None of these 

Model 5 :

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

Solution :

25% = 1/4 ain

=> 5/4 CP = SP = 450

CP = (4/5) x 450 = 360

Practice Problems on Model 5

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

Model 6 :

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

Solution :

6 1/4% = 25/400 = 1/16 

=> 15/16 CP  [Note : for Loss we should write difference / denominator]

=> 15/16 CP = 375

=> CP = 400

Practice problems on Model 6 :

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

Model 7 :

1. 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 ?
1. Rs. 20,000
2. Rs. 22,500
3. Rs. 25,000
4. Rs. 27,750
5. None of these 

Solution :

Assume that the cost price for A is a 

=> a x (110/100) x (80/100) = 22000

=> a. 22/25 = 22000

=> a = 25000

Practice Problems on Model 7 :

1. 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 ?
1. Rs. 30,000
2. Rs. 32,500
3. Rs. 35,000
4. Rs. 37,750
5. None of these 
2. 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 ?
1. Rs. 20,000
2. Rs. 20,500
3. Rs. 21,000
4. Rs. 19,600
5. None of these 
3. 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 ?
1. Rs. 1,00,000
2. Rs. 1,12,000
3. Rs. 1,20,000
4. Rs. 1,16,000
5. None of these 

Model 8 :

1. The cost price of an object is numerically equal to its profit % and its selling price is Rs. 56. What is its cost price ?
1. Rs. 20
2. Rs. 36
3. Rs. 40
4. Rs. 50
5. None of these 

Solution :

For these type of problems, you can check directly from given answer options

Here, the cost price is numerically equal to it's profit %, 

so assume the cost price = Rs. x, 

So profit % = x%

=> ((100+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

So, Option 3 is the correct answer.

 

Practice Problems on Model 8 :

1. 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 ?
1. Rs. 20
2. RS. 36
3. Rs. 40
4. Rs. 50
5. None of these 
2. 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 ?
1. Rs. 15
2. Rs. 25
3. Rs.28
4. Rs. 30
5. None of these 
3. The cost price of an object is numerically equal to its profit % and its selling price is Rs. 77.36. What is cost price ?
1. Rs. 56
2. Rs. 54
3. Rs. 66
4. Rs. 64
5. None of these 

Model 9 :

1. 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 ?
1. Rs. 49
2. Rs. 50
3. Rs. 48
4. RS. 46
5. None of these 

Solution :

Find the average 

=> (56 + 42) / 2 = 98 / 2 = 49

Practice Problems on Model 9 :

1. 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 ?
1. Rs. 30
2. Rs. 32
3. RS. 25
4. Rs. 28
5. None of these 
2. 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 ?
1. Rs. 149
2. Rs. 199
3. Rs. 201
4. Rs. 211
5. None of these
3. 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 ?
1. Rs. 49
2. Rs. 50
3. Rs. 48
4. Rs. 46
5. None of these

Model 10 :

1. 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 ?
1. Rs. 42
2. Rs. 40
3. Rs. 38
4. Rs. 36
5. None of these 

Solution :

CP = 30+Loss = 48-Profit 

=> Loss + Profit = 48-30 = 18

 => L + 2L = 18  => L = 6

CP = 30+6 = 36

Practice Problems on Model 10 :

1. 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 ?
1. Rs. 42
2. Rs. 40
3. Rs. 38
4. Rs. 36
5. None of these 
2. 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 ?
1. Rs. 42
2. Rs. 40
3. Rs. 38
4. Rs. 36
5. None of these 
3. 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 ?
1. Rs. 42
2. Rs. 40
3. Rs. 38
4. Rs. 36
5. None of these 

Model 11 :

1. 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 ?
1. Rs. 4.95
2. Rs. 5
3. Rs. 9.90
4. Rs. 10
5. 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 :

1. 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 ?
1. Rs. 9.60
2. Rs. 20
3. Rs. 19.20
4. Rs. 10
5. None of these 
2. 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 ?
1. Rs. 500
2. Rs. 990
3. Rs. 1000
4. Rs. 960
5. None of these 
3. 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 ?
1. Rs. 4000
2. Rs. 2000
3. Rs. 3600
4. Rs. 1800
5. None of these

Model 12 :

1. The cost price of 3 articles is same as the selling price of 2 articles. What is the loss or gain % ?
1. 50% loss
2. 50% gain
3. 25% loss
4. 25% gain
5. 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 

=> 3x = 2y

 

=> 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 :

1. The cost price of 2 articles is same as the selling price of 3 articles. What is the loss or gain % ?
1. 50% loss
2. 33 1/3% gain'
3. 25% loss
4. 33 1/3% loss
5. None of these 
2. The cost price of 13 articles is same as the selling price of 12 articles. What is the loss or gain % ?
1. 8 1/3 % gain
2. 12 2/3 % gain
3. 8 1/3% loss
4. 12 2/3 % loss
5. None of these
3. The cost price of a dozen articles is same as the selling price of a score articles. What is the loss or gain % ?
1. 50% loss
2. 50% gain
3. 40% loss
4. 40% gain
5. 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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