Home / Aptitude / Profit and Loss / Basic Concepts and Questions
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Cost Price (CP): The price at which a commodity is purchased is called the cost price
Selling Price (SP) : The price at which a commodity is sold is called the selling price
The difference between cost price and selling price gives loss or profit.
If the selling price of a commodity is more than the cost price then it is a profit. (SP>CP)
If the cost price of a commodity is more than the selling price then it is a loss (CP>SP)
Profit = SP  CP
Loss = CP  SP
Cost Price = Selling Price  Profit
Selling Price = Cost price + Profit
When loss is known,
Cost price = Selling price + Loss
Selling price = Cost price  Loss
If the selling price is equal to the cost price then there is neither Profit nor Loss
5.2 Percentage profit is determined by calculated the profit obtained for hundred.
. Suppose a person buys an article and sells it for a price more than what he had invested. He then gains in This transaction. Here the investment is nothing but the cost price. To determine the extent of the benefit, we define Percentage profit.
${\mathbf{Profit}}{\mathbf{}}{\mathbf{\%}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{Profit}}{\mathbf{Cost}\mathbf{}\mathbf{Price}}{\mathbf{\times}}{\mathbf{}}{\mathbf{100}}$
${\mathbf{Loss}}{\mathbf{}}{\mathbf{\%}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{Loss}}{\mathbf{Cost}\mathbf{}\mathbf{Price}}{\mathbf{\times}}{\mathbf{}}{\mathbf{100}}$
Example 1: A shopkeeper buys an article for ₹ 250 and sells it for ₹ 300. Find his profit percentage.
CP = ₹ 250 SP = ₹ 300
Profit = SP  CP
then profit amount = ₹ 300  ₹ 250 = ₹ 50
${\mathbf{Profit}}{\mathbf{}}{\mathbf{\%}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{50}}{\mathbf{250}}{\mathbf{\times}}{\mathbf{}}{\mathbf{100}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{20}}{\mathbf{\%}}$
Example 2: A shopkeeper buys an article for ₹ 250 and sells it for ₹ 225. Find his loss percentage.
CP = ₹ 250 SP = ₹ 225
Loss = CP  SP
then Loss amount = ₹ 250  ₹ 225 = ₹ 25
${\mathbf{Loss}}{\mathbf{}}{\mathbf{\%}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{25}}{\mathbf{250}}{\mathbf{\times}}{\mathbf{}}{\mathbf{100}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{10}}{\mathbf{\%}}$
NOTE : FOR MORE CONCEPTS, WATCH THE VIDEO.
Q1. 
A man sold a watch for ₹ 1500 which he bought at ₹ 1550. His profit or loss is : 
A. ₹ 500 profit 

B. ₹ 500 loss 

C. ₹ 50 profit 

D. ₹ 50 loss 
CP = ₹ 1550 SP = ₹ 1500
SP is less than Cp
Hence, Loss = 1550  1500 = ₹ 50
Q2. 
If a shopkeeper buys an article for ₹ 800 and sells it for ₹ 900. Find his profit percentage. 
A. 12.5 % loss 

B. 125 % profit 

C. 1.25 %profit 

D. 12.5 % profit 
CP = ₹ 800 SP = ₹ 900
Profit = SP  CP
then profit amount = ₹ 900  ₹ 800 = ₹ 100
$\mathrm{Profit}\%=\frac{100}{800}\times 100=12.5\%$
Q3. 
Sudhanshu buys a book ₹ 600 and sells it for ₹ 500. Find his profit or loss percentage. 
A. 20 % profit 

B. 20 % loss 

C. 16.66 % loss 

D. 16.66 % profit 
CP = ₹ 600 SP = ₹ 500
Loss = CP  SP
Loss amount = ₹ 600  ₹ 500 = ₹ 100
$Loss\%=\frac{100}{600}\times 100=16.66\%$
Q4. 
Jeeban buys a camera at ₹ 4000. By selling it, he incurs a loss of 5%. What is his selling price? 
A. ₹ 3800 

B. ₹ 4200 

C. ₹ 4500 

D. ₹ 3750 
Loss amount = 4000 × ^{5}/_{100} = 200
SP = 4000  200 = ₹ 3800
Or
CP = 100 % SP = 95 %
SP = 4000 × ^{95}/_{100} = ₹ 3800
Q5. 
Harish sold his bike for ₹ 62500 and made a profit of 25%. At what price did he buy it? 
A. ₹ 46875 

B. ₹ 48500 

C. ₹ 50500 

D. ₹ 50000 
CP = 100 % SP = 125 %
125 % = ₹ 62500
100 % = ^{62500}/_{125} x 100 = ₹ 50000
Or
CP = 1 Profit = ^{1}/_{4} Sp = ^{5}/_{4}
CP = 62500 x ^{4}/_{5} = ₹ 50000
Q6. 
Rajiv sold his old camera at ₹ 6000 and got a profit of 20%. What was the cost price of the camera? 
A. ₹ 4800 

B. ₹ 5000 

C. ₹ 4500 

D. ₹ 5500 
CP = 100 % SP = 120 %
120 % = ₹ 6000
100 % = ^{6000}/_{120} x 100 = ₹ 5000
Q7. 
A person bought a TV set for ₹ 12000 and sold it at a loss of 12.5%. Find the selling price of the TV set. 
A. ₹ 10050 

B. ₹ 15050 

C. ₹ 10500 

D. ₹ 10005 
Loss amount = 12000 × ^{12.5}/_{100} = 1500
SP = 12000  1500 = ₹ 10500
Or
CP = 100 % SP = 87.5 %
SP = 7000 × ^{87.5}/_{100} = ₹ 10500
Or
CP = 1 , Loss = 12.5% = 1/8, Sp = ^{7}/_{8}
SP = 12000 × ^{7}/_{8} = ₹ 10500
Q8. 
Pawan bought a cycle at ₹ 7000. For how much should he sell it to gain 15%. 
A. ₹ 7750 

B. ₹ 8050 

C. ₹ 8550 

D. ₹ 8005 
Profit amount = 7000 × ^{15}/_{100} = 1050
SP = 7000 + 1050 = ₹8050
Or
CP = 100 % SP = 115 %
SP = 7000 × ^{115}/_{100} =₹ 8050
or
SP = 7000 × 1.15 = ₹ 8050
Q9. 
Rajesh sold his electronic typewriter at ₹ 7500 which he bought at ₹ 8000. Calculate his profit or loss percentage. 
A. 6.66% loss 

B. 6.66% profit 

C. 6.25% profit 

D. 6.25% loss 
CP = ₹ 8000, SP = ₹ 7500.
Therefore, Loss = ₹ 8000  ₹ 7500 = ₹ 500
Loss % = $\frac{500}{8000}\times 100=6.25\%$
Q10. 
If a shopkeeper buys an article for ₹ 500 and sells it for ₹ 450. Find his loss percentage. 
A. 20% 

B. 10% 

C. 25% 

D. 40% 
CP = ₹ 500 SP = ₹ 450
Loss = CP  SP
Loss amount = ₹ 500  ₹ 450 = ₹ 50
$Loss\%=\frac{50}{500}\times 100=10\%$
Q11. 
If a shopkeeper buys an article for ₹ 250 and sells it for ₹ 350. Find his profit percentage. 
A. 60% 

B. 80% 

C. 75% 

D. 40% 
CP = ₹ 250 SP = ₹ 350
Profit = SP  CP
then profit amount = ₹ 350  ₹ 250 = ₹ 100
$\mathrm{Profit}\%=\frac{100}{250}\times 100=40\%$
Q1. 
A fruit vendor buys 42 apples for ₹350. He sells 28 of these at ₹10 each and the remaining at ₹98. Find his profit or loss percent. 
A. 5% loss 

B. 5% profit 

C. 8% loss 

D. 8% profit 
Total CP = ₹350
SP = ₹28$\times $10 $+$ 98 = ₹378
SP is more than CP.
Profit = ₹378  ₹350 = ₹28
Profit % = $\frac{28}{350}\times 100=8$%
Q2. 
A fruit vendor buys 20 oranges for ₹125. At what price should he sell each orange to get a profit of 12%? 
A. ₹ 6 

B. ₹ 8 

C. ₹ 7 

D. ₹ 9 
The cost price of each orange = $\frac{125}{20}=\frac{25}{4}$
To get a profit of 12%, he needs to sell at 112%.
Hence, the selling price of each orange = $\frac{25}{4}\times \frac{112}{110}=7$
Q3. 
A man sold an article for ₹ 800 at a profit of 60%. Find his cost price. 
A. ₹ 1260 

B. ₹ 1000 

C. ₹ 500 

D. ₹ 1160 
CP=100 % SP = 160 %
160 % = ₹ 800
100 % = $\frac{800}{160}\times 100=500$
Q4. 
By selling 20 articles for a rupee, a man losses 4%. How many articles for a rupee should he sell so as to make a gain of 20%? 
A. 18 

B. 16 

C. 12 

D. 15 
Selling price of each article =$\frac{1}{20}$
96 % = $\frac{1}{20}$
120 % =$\frac{1}{20\times 96}\times 120=\frac{1}{16}$ (Price of 1 article)
Hence 16 for a rupee
Q5. 
Raj sold an item for ₹ 6384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%? (SBI PO 2017) 
A. ₹ 14656 

B. ₹ 11856 

C. ₹ 13544 

D. Can't be determined 
CP = 100% Loss = 30% SP = 70%
To get a profit of 30%, SP should be 130%
70% = 6384
130% = $\frac{6384}{70}\times 130=11856$ (Ans)
Q6. 
A shopkeeper purchased a TV for ₹ 2000 and a radio for ₹ 750. He sells the TV at a profit of 20% and the radio at a loss of 5%. The total gain or loss is : (SBI CLERK  2016) 
A. ₹ 352.50 gain 

B. ₹ 362.50 gain 

C. ₹ 332 gain 

D. ₹ 300 loss 
Total CP = 2000 + 750 = 2750
Total SP = $2000\times \frac{120}{100}+750\times \frac{95}{100}=3112.5$
Total gain = 3112.5  2750 = ₹ 362.5
Q7. 
A shopkeeper sold an article for ₹ 1380 at a loss of 8%. At what price should it be sold to get a profit of 8%? (SBI CLERK  2016) 
A. ₹ 1560 

B. ₹ 1620 

C. ₹ 1680 

D. ₹ 1740 
CP = 100% Loss = 8% SP = 92%
To get a profit of 8%, SP should be 108%
92% = 1380
108% = $\frac{1380}{92}\times 108$ = ₹ 1620 (Ans)
Q8. 
Sugan sold his bicycle at a loss of 30% at ₹ 10500. At what price should he have sold it so as to get a profit of $6\frac{2}{3}\%$? 
A. ₹ 18000 

B. ₹ 24000 

C. ₹20000 

D. ₹ 16000 
CP = 100% Loss = 30% SP = 70%
70% = 10500
100% = $\frac{10500}{70}\times 100$ = 15000
Profit = $6\frac{2}{3}\%$ = $\frac{1}{15}$
SP = 1 + $\frac{1}{15}$= $\frac{16}{15}$ of CP = 15000 $\times \frac{16}{15}$= ₹ 16000
Q9. 
By selling a TV set for ₹ 12000, a dealer makes a loss of $14\frac{2}{7}\%$. At what price should he have sold it so as to get a profit of $7\frac{1}{7}\%$? 
A. ₹ 13000 

B. ₹ 14000 

C. ₹ 15000 

D. ₹ 16000 
$14\frac{2}{7}\%$ = $\frac{1}{7}$ $7\frac{1}{7}\%=\frac{1}{14}$
Profit % and Loss % are given in fraction.
Hence, we take the CP = 1
Loss = $\frac{1}{7}$ SP = 1  $\frac{1}{7}$= $\frac{6}{7}$
Profit = $\frac{1}{14}$ SP = 1 + $\frac{1}{14}$= $\frac{15}{14}$
As per the question, $\frac{6}{7}$ = 12000
$\frac{15}{14}$ = $12000\times \frac{7}{6}\times \frac{15}{14}=\u20b915000$
Q1. 
The selling price of a chair, a desk, and a table are in the ratio of 9: 5: 8. The cost price of the chair is ₹ 400. The profit percentage earned by selling the table is $14\frac{2}{7}\%$. If the ratio of the percentage profit earned by selling the chair, desk, and table is 7: 14: 8 respectively, what is the overall percentage profit? 
A. 16.58% 

B. 15. 79% 

C. 14.75% 

D. 13.76% 
ratio of the percentage profit is 7 : 14 : 8
8 = 1/7 ( 14.28%)
7 = 1/8
14 = 1/4
The CP of the chair = 400, Its SP = 400 x ^{9}/_{8} = 450
The ratio of SP = 9 : 5 : 8
9 = 450
5 = 250
8 = 400
Total SP = 1100
CP of desk = 250 x 4/5 = 200
CP of table = 400 x 7/8 = 350
Total CP = 400 + 200 + 350 = 950
Profit = 1100  950 = 150
Profit % = 150/950 x 100 = 15.789% = 15.79%