PROFIT AND LOSS Important Formulas Cost Price The price, at which an article is purchased, is called its cost price, abbreviated as C.P. Selling Price The price, at which an article is sold, is called its selling prices, abbreviated as S.P. Profit or Gain If S.P. is greater than C.P., the seller is said to have a profit or gain.
Loss If S.P. is less than C.P., the seller is said to have incurred a loss.
Loss or gain is always reckoned (Calculated) on C.P.
Selling Price
If an article is sold at a gain of say 20%, then S.P. = 120% of C.P.
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If an article is sold at a gain of say 35%, then S.P. = 135% of C.P. If an article is sold at a loss of say, 20% then S.P. = 80% of C.P. If an article is sold at a loss of say, 35% then S.P. = 65% of C.P. Cost Price
Dishonest dealers & False weights A dishonest dealer sells his goods at cost price, but he uses false weights, Then the % of gain or profit is
Selling at the same price Suppose a person sells two objects at the same price, one at a profit of another at a profit of %, then
%&
Suppose a person sells two objects at the same price, one at a profit of
%&
another at a Loss of
%, then
Suppose a person sells two objects at the same price, one at a Loss of another at a Loss of % , then
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%&
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Suppose a person sells two objects at the same price, one at a Profitof %& another at a Loss of %, then he always incurs a net loss, expressed as
A trader purchases
articles for
and sells
articles for
then,
If Cost price of X articles is same as Selling Price of Y articles , Then
Marked Price & Discount The Price on the label of an article is called its Marked Price (M.P) or List Price. The Deduction in the Marked Price (M.P) is called Discount (D)
Discount percentage Discount % is the discount expressed as a percentage of Marked Price (M.P)
S.P = M.P
M.P = S.P
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Successive Discounts If , %& % are successive discounts on M.P, Then
Single equivalent discount of 2 successive discounts
Single equivalent discount of 3 successive discounts
When discount and profit is given , then
When Discount % and Profit % are given, then C.
M.P = C.P
Successive Gains If a salesman gets successive gains of x% & y% , then his actual gain is
G%=x+y+
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Solved Examples 1. Rahul purchased a hard disk for Rs.6,900 and sold it for a loss of 12%. What is the selling price of the hard disk? Solution:
C.P = 6900 L = 12 %
= 6900 = 69 = Rs. 6,072 2. A man buys a toy for Rs. 25 and sells it for Rs. 30. Find his gain percent. Solution: C.P = Rs.25 S.P = Rs.30
Profit or Gain %
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3. By selling a watch for Rs. 144 a man loses 10%. At what price should he sell it in order to gain 10%? Solution:
S.P. = Rs. 144; Loss = 10%
Now the C.P is Rs.160, in order to gain 10%, the selling price should be 10% more than the C P … Hence
= 16 =Rs. 176 4. By selling an article for Rs. 100, one gains Rs. 10. Then the gain percent is Solution:
S.P = Rs.100 C.P = S.P P =100-10 =Rs. 90
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Profit or Gain %
5. A person buys 100 cups at Rs. 10 each. On the way 10 cups are broken. He sells the remaining cups at Rs. 11 each. His loss percent is…. Solution:
Loss %
6. A loss of 5% was suffered by selling a plot for Rs. 4,085. The cost price of the plot Was ____? Solution:
L = 5% S.P = Rs.4085
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7. By selling a vehicle for Rs. 36,300, a person gains 21% profit. What was his gain in Rupees? Solution
S.P = Rs. 36,300 P%=21%
8. Hameed bought a calculator for Rs. 520 and sold it with 15% profit on the price he bought. At what price did he sell the calculator? Solution:
C.P = Rs.520 P% = 15%
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9. Nimesh bought a cycle for Rs. 1,850.He spent Rs.380 for buying different accessories. Approximately, at what price should he sell the cycle to make 20% profit in the transaction? Solution:
C.P = 1850+380 = Rs. 2230 P = 20%
10. Peter purchased a machine for Rs. 80,000 and spent Rs. 5000 on repair and Rs. 1000 on transport and sold it with 25% profit. At what price did he sell the machine? Solution:
C.P. = Rs. (80000 + 5000 + 1000) = Rs. 86000 Profit = 25%.
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11.On selling an article for Rs 170, a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees………….. Solution
Let,
SP = Rs. 170 L = 15%
12. A dishonest dealer claims to sell his goods at cost price, but he uses a weight of 960gm for the kg weight. His gain percent is? Solution
Error = 1000 – 960 = 40 gms
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13. A dishonest dealer sells his goods at the cost price but still earns a profit of 25%. by underweighing. What weight does he use for a kg ? Solution:
P% = 25 True Value = 1000 gms. Let, Error = E False weight or Value = True Value – Error
Error = 200 False weight = True value – Error = 1000 – 200 => 800 gms.
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14. A dishonest dealer to sell his goods at cost price, but he uses a weight of 960 grams foe the Kg weight. then the percentage of gain or profit is Solution:
True Value = 1000 gms Error = True Value – False value = 1000 – 960 = 40 gms.
15. Two objects are sold at the same price one at a profit of 10% & another at a profit of 32%, Then what is the Net Profit % ? Solution:
=10% = 32%
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16. Two objects are sold at the same price one at a profit of 40% & another at a loss of 16%, Then what is the Net Profit % ? Solution:
=40% = 16%
17. Two objects are sold at the same price one at a profit of 20% & another at a loss of 28%, Then what is the Net Profit or loss % ? Solution:
=20% = 28%
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18. Two objects are sold at the same price one at a loss of 10% & another at a loss of 28%, Then what is the Net Profit % ? Solution:
=10% = 28%
19. A man sells two tables at the same price. On one he makes a profit of 10% and on the other he suffers a loss of 10%. His loss per cent on the whole transactions is? Solution:
20.A car and a jeep were sold for Rs. 125000 each. The car was sold at a loss of 20% while the jeep at a gain of 20%. The entire transaction resulted in…. Solution:
In these kind of cases where two items are sold, one at profit and other at loss where profit% is equal to loss%, there will always be loss.
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In this case x = 20 So loss in whole transaction is
21. Two objects are sold at the same price one at a loss of 22% & another at a loss of 22%, Then what is the Net Loss% ? Solution:
22. A shopkeeper purchases 12 balloons for Rs. 10 and sells them at 10 balloons for Rs.12. Thus, he earns a profit of? Solution:
= 12 = Rs.10 =10
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= Rs.12
= 44 % 23. A man buys pencils at 10 for Rs. 3 and sells at 8 for Rs. 3. His gain percent is? Solution:
= 10 = Rs.3 =8 = Rs.3
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24. The cost price of 400 lemons is equal to the selling price of 320 lemons. Then the profit percent is Solution: X = 400 , Y = 320
=25% 25. The cost price of 10 articles is equal to the selling price of 9 articles. Find the gain% Solution: X = 10 Y=9
26. The selling price of 10 oranges is the cost price of 13 oranges. Then the profit percentage is…. Solution:
Let ,
No.of Oranges Purchased( X) = 13 No.of Oranges Sold (Y) = 10
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P
t
27. A bag marked at Rs.80 & is sold for Rs.68. The rate of discount is ? Solution:
M.P = Rs.80 S.P = Rs.68 D = M.P – S.P = 80 – 68 = Rs.12
=
×100
= 15 % 28. The marked price of an article is Rs.500. It is sold at successive discounts of 20% and 10%. The selling price of the article (in rupees) is? Solution:
20% 10%
S.P = 500
=5
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=5 = Rs.360 29. The successive discounts of 10% and 20% are equivalent to a single discount of? Solution:
= 10 = 20
%
30. A discount series of 10%, 20% and 40% is equal to a single discount of ..... Solution:
Equivalent single discount
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31. There are two consecutive discounts of 35% and 10% on a saree. If a person paid Rs.1170 for that, then what was the original price of the saree before the discounts? Solution:
S.P = Rs.1170 = 35% = 10% M.P = ?
2000 = M.P M.P = Rs.2000 32. A trader gives two successive discounts of 15% and 10% on the marked price of an article. If the selling price is Rs 765, the marked price is….
Solution:
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33. Listed price of an article is Rs. 65. A customer pays Rs. 56.16 for it. He was given two successive discounts. If the first discount is 10% find the second . Solution:
96 = 100 -
34. A single discount equivalent to a discount series of 20%,10% and 25% is Solution:
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35. A trader allows two successive discounts of 20% and 10%. if he sells an article for Rs.108, then the marked price of the article is Solution:
= M.P 150 = M.P M.P = Rs.150 36. A retailer purchased radio sets at the rate of Rs. 400 each from a wholesaler. He raised the price by 30% and then allowed a discount of 8% on each set. His profit will be…. Solution:
CP = Rs 400 P = 30%
SP = 400 =400 =4
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= 520
37. A retailer purchases a grinder at a discount of 15% and sells it for Rs 1955 at a profit of 15%. The amount of discount received by the retailer from the wholesaler was…. Solution:
Profit% = 15% SP = 1955, CP = ?
Profit or Gain %
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2000 = MP MP = Rs. 2000 Discount = 15% of 2000 = Rs 300 38. The cost price of an article is Rs. 800. After allowing a discount of 10%, a gain of 12.5% was made. Then the marked price of the article is…. Solution:
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39. An article listed at Rs. 800 is sold at successive discounts of 25% and 15%. The buyer desires to sell it off at a profit of 20% after allowing a 10% discount. What would be his list price? Solution:
40. A manufacturer marked an article at Rs. 50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was…. Solution:
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Profit or Gain %
42. An article is sold at a discount of 20% and an additional discount of 30% is allowed on cash payment. If Vidya purchased the article by paying Rs 2240 in cash, the marked price of the article was…. Solution:
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43. A plate was sold for Rs. 6,300 after giving two successive discounts of 12.5% and 10%. Find the marked price. Solution:
Let
S.P = Rs. 6,300 = 12.5 = 10
44. A shopkeeper buys an article for Rs. 450. He marks it at 20% above the cost price. Find the percentage discount given by him if he sells the article for Rs. 496.80. Solution:
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45. The list price of a shirt is Rs 440 and a customer pays Rs 396 for it. The discount rate is...... Solution:
MP = Rs. 440 & SP = Rs.396
46. An article is listed at Rs 920. A customer pays Rs 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is…. Solution:
5
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47. If a salesman gets successive gains of 15% & 20%, then his actual gain ? Solution:
X= 15% Y= 20%
G%=x+y+
= 15 + 20 +3 = 38% 48. The marked price of a radio is Rs. 480. The shopkeeper allows a discount at 10% and gains 8%. If no discount is allowed, his gain percent would be…. Solution:
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49. A’ sells an article to ‘B’ at a profit of 20% and ‘B’ sells it to ‘C’ at a profit of 25%. If ‘C’ pays Rs. 1,200, the cost price of the article originally (in Rs.) is…. Solution:
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