Profit and Loss Basic: Concept
The Profit and Loss (P&L) is used to determine the market price of a commodity and the profitability of a firm. Every product has a cost and a selling price. Based on these pricing, we could calculate the profit or loss for a specific product. The key words discussed here include cost price, fixed, variable, and semi-variable cost, selling price, marked price, list price, margin, & so on.
Cost Price: The amount paid for an item is called its cost price, abbreviated as C.P.
Selling Price: The amount it is sold for is called its selling price, abbreviated as S.P.
Profit or Gain: If the Selling Price is greater than the Cost Price, the seller is said to have a profit or gain.
Loss: If the Selling Price is less than the Cost Price, the seller is said to have incurred a loss.
Marked Price Formula (MP): This Price is labelled by shopkeepers to offer a discount to the customers.
Profit and Loss Important Formulas
| Profit and Loss Terms | Formulas |
| $$Discount$$ | $$Marked \ Price – Selling \ Price$$ |
| $$Discount \%$$ | $$ \frac{Discount}{Marked\ price}\times 100 $$ |
| $$Gain $$ | $$Selling \ Price – Cost \ price$$ |
| $$Gain \%$$ | $$ \frac{Gain}{Cost\ price} \times100$$ |
| $$Loss$$ | $$Cost \ price – Selling \ Price$$ |
| $$Loss\%$$ | $$ \frac{Loss}{Cost\ price} \times100$$ |
| $$Selling\ Price: (S.P.) (if S.P > C.P)$$ | $$(\frac{100+gain\%}{100})\times C.P$$ |
| $$Selling\ Price: (S.P.) (if S.P < C.P)$$ | $$(\frac{100+loss\%}{100})\times C.P$$ |
| $$Cost\ Price: (C.P.) (if S.P > C.P)$$ | $$(\frac{100}{100+gain\%})\times S.P$$ |
| $$Cost\ Price: (C.P.) (if S.P < C.P)$$ | $$(\frac{100}{100+Loss\%})\times S.P$$ |
| When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by: | $$(\frac{x}{10})^2$$ |
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If a trader professes to sell his goods at cost price, but uses false weights, then Gain% |
$$[\frac{error}{True\ value – error}\times 100]\%$$ |
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If there are two successful profits, say x% and y%, then the net percentage profit equals to |
$$[x+y+(\frac{xy}{100})]$$ |
| If the profit is x%, and loss is y%, then the net percentage of profit or loss will be | $$[x-y-(\frac{xy}{100})]$$ |
Practice Quizzes
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Profit and Loss Quiz 1 – Coming Soon |
Profit and Loss Quiz 2 – Coming Soon | Profit and Loss Quiz 3 – Coming Soon |
Sample Questions
Q1) A person buys a bicycle of Rs. 4600 and he went for repair. A selling price of an article is Rs. 5300 at 6% profit. Find the repairing cost.
a) Rs. 100
b) Rs. 300
c) Rs. 400
d) Rs. 200
Answer: C
Let the repairing cost be x,
Profit % = (SP – CP)/ CP × 100
6 = (SP/CP – 1) × 100
6/100 = (SP/CP – 1)
3/50 = (SP/CP – 1)
1 + 3/50 = SP/CP
53/50 = 5300/ (4600 + x)
1/50 = 100/ (4600 + x)
(4600 + x) = 100 × 50
(4600 + x) = 5000
x = 5000 – 4600
x = 400
Repairing cost is Rs. 400
Q2) A man purchase a table fan for Rs. 120/-. Find the selling price if he incurred a loss of 5%.
a) Rs. 114/-
b) Rs. 120/-
c) Rs. 130/-
d) Rs. 140/-
Answer: A
Loss% = (CP – SP)/CP × 100
5 = (CP – SP)/CP × 100
5/100 = 1 – SP/CP
1/20 = 1 – SP/120
1 – 1/20 = SP/120
19/20 = SP/120
SP = 114/-
Q3) Cost Price of a Book is Rs. 3000 at loss of 20%. Find the selling price.
a) Rs. 2500
b) Rs. 1200
c) Rs. 2000
d) Rs. 2400
Answer: D
Loss % = (CP – SP)/CP × 100
20 = (1 – SP/CP) × 100
20/100 = (1 – SP/CP)
1/5 = (1 – SP/CP)
1 – 1/5 = SP/CP
4/5 = SP/3000
SP = 2400
Q4) The cost price of textbook is Rs. 60 and selling price of the textbook is Rs. 90. Find the profit percent of the textbooks.
a) 40%
b) 30%
c) 50%
d) 20%
Answer: C
Profit % = (SP – CP)/ CP × 100
= (90 – 60)/ 60 × 100
= 30/60 × 100
= 100/2
= 50%
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Q5) A cost price of bike is Rs. 1200/- and repairing cost is Rs. 300/-. Selling price of bike is Rs. 2000/-. Find the profit percent.
a) 11.11%
b) 9.09%
c) 66.67%
d) 33.34%
Answer: D
CP = 1200 + 300 = Rs. 1500/-, SP = Rs. 2000/-
Profit Percent = (SP – CP)/ CP × 100
= (2000 – 1500)/ 1500 × 100
= 500/1500 × 100
= 100/3
= 33.34%
Q6) A selling price of a box is Rs. 2600/- at 30% profit. Find the cost price.
a) Rs. 1500/-
b) Rs. 1800/-
c) Rs. 2000/-
d) Rs. 2500/-
Answer: C
Profit % = (SP – CP)/ CP × 100
30 = (SP/ CP – 1) × 100
30/100 = (SP/ CP – 1)
3/10 = (SP/ CP – 1)
1 + 3/10 = SP/ CP
13/10 = SP/ CP
13/10 = 2600/CP
CP = 2000/-
Q7) Cost price of 120 gram gold is equal to selling price of 150 gram gold. Find the profit or loss percent.
a) 15%
b) 20%
c) 25%
d) 30%
Answer: B
According to the article,
120 × CP = 150 × SP
SP/ CP = 120/150 = 4/5
Loss% = (CP – SP)/ CP × 100
= (1 – SP/CP) × 100
= (1 – 4/5) × 100
= 100/5
= 20%
Q8) Difference between selling price at 5% profit and 8% loss is Rs. 104/-. Find the cost price.
a) Rs. 850/-
b) Rs. 900/-
c) Rs. 700/-
d) Rs. 800/-
Answer: D
According to the question,
105/100 × CP – 92/100 × CP = 104
105 × CP – 92 × CP = 10400
13 × CP = 10400
CP = 10400/13
CP = Rs. 800/-
These are some example problems on profit and loss, we hope you like it.