Profit and Loss

Profit and Loss  Aptitude basics, practice questions, answers and explanations

Profit=SP-CP
Loss=CP-SP
Profit %= (Profit/CP) *100
Loss %= (Loss/ CP) *100
Discount= MP-SP
Discount %= (discount/ MP) * 100
where SP= Selling Price, CP= Cost Price, MP= Marked Price

Exercise questions

1. A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

A) 33.33%     

B) 75%      

C) 300%     

D)150%

Solution:-profit=SP of 75 articals CP=SP of 25 articals and SP=SP of 100 articals

Profit%=(profit/CP) *100=((10-25)/25)*100=300%

2. A merchant buys two articles for Rs.600. He sells one of them at a profit of 20% and the other at a loss of 10% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

A) Rs. 400    

B) Rs.440     

C) Rs. 536.80                

D) Rs. 160

Solution:- Assume that the cost prices be x and y

Total cost price=600=x+y……(1)

Total selling price=120% of x+90% of y

But he get no profit/loss

600=120% of x+90% of y

4x+3y=2000……(2)

Now solve equations (1) and (2) for y

Y=400 Rs.

3. A trader professes to sell his goods at a loss of 10% but weights 900 grams in place of a kg weight. Find his real loss or gain per cent.

A) 2% loss  

B) 0.00% gain

C) 2% gain  

D)None of these

Solution:- Use the following formula

(100+g)*Faulty measure=(100+x)*True measure

Where,

g-overall gain/loss

x-profit or loss (as per CP & SP)

here we have x=-10 (loss) ,g=? ,true measure=1000gm, faulty measure=900gm

now put the given values in to the formula

(100+g)*900=(100-10)*1000

100+g=900/9

G=0.00%

4. If apples are bought at the rate of 30 for Rs.100.  How many apples must be sold for Rs.100 so as to gain 20%?

A) 28    

B)25         

C) 20        

D) 22

Solution:- To gain 20% profit he will have to sell the 30 apples for 120 Rs. Assume that he sells x number of apples for Rs. 100

i.e:- 120% of x=30

120/100*x=30  è x=30*100/120=25

That means to have 20% profit he will sell 25 apples for 100 Rs.

5.Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?

A) Rs. 40      

B) Rs. 45 

C) Rs. 36 

D)Rs. 28

Solution:- Given, SP=56 ,CP=X ,Profit%=X%

we know that

Profit%=(profit/CP)*100

X=[(56-X)/X]*100

X^2+100X-5600=0……..solve for X

X=CP=40

6. One year payment to the servant is Rs. 200 plus one shirt.  The servant leaves after 9 months and receives Rs. 120 and a shirt. Then find the price of the shirt.

A) Rs. 80

B) Rs. 100

C) Rs. 120

D) Cannot be determined

Solution:- Let x be the price of the shirt then

payment for 12 months=200+x

payment for 1 month=(200+x)/12………(1)

but, payment for 9 months=120+x

payment for 1 month=(120+x)/9…………..(2)

from (1) & (2)

(200+x)/12=(120+x)/9

Solve for x and we get

X=120

7. Two merchants sell, each an article for Rs.1000. If Merchant A computes his profit on cost pricwhile Merchant B computes his profit on selling price, they end up making profits of 25% respectively. By how much is the profit made by Merchant B greater than that of Merchant A?

A) Rs.66.67

B) Rs. 50         

C) Rs.125         

D) Rs.200

Solution:- SP1=SP2=1000

Merchant A =CP+Profit=1000

if profit%=25%

èprofit=200…….merchant A

Profit=25% of 1000=250…….merchant B

Difference=250-200=50

8. A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?

A) 25%         

B)50%         

C) 100%         

D)66.67%

Solution:- here CP=SP of 25 articles and SP=SP of 50 articles èprofit=SP of 25 articles

Hence profit%=100%

9. A merchant marks his goods up by 75% above his cost price. What is the maximum % Amount that he can offer so that he ends up selling at no profit or loss?

A)75%         

B) 46.67%         

C) 300%         

D)42.85%

Solution:-Assume that the CP=100 & SP=175 also assume that he reduces x% amount to get no profit  no loss.

X% of 175=100

 X=400/7

That means he will offer=100-400/7=300/7=42.85%

10. A merchant marks his goods up by 75% above his cost price. What is the maximum % Amount that he can offer so that he ends up selling at no profit or loss?
A)75%         
B) 46.67%         
C) 300%         
D)42.85%

Solution:-Assume that the CP=100 & SP=175 also assume that he reduces x% amount to get no profit  no loss.

X% of 175=100

X=400/7

That means he will offer=100-400/7=300/7=42.85%

11. A dealer buys a product at Rs.1920. he sells at a discount of 20% still he gets teh profit of 20%. what is the selling price?   ( 1 Marks )

A)  534

B)  2300

C)  2304

D) 2403

Solution:- cost price is 1920
now discount part is to confuse you because the actual selling price will never
depend on discount
so 20% of 1920 is 384
and adding the profit to calculate selling price 1920+384=2304

12. Mani sells vegetables and he marks up the prices at 5% above his cost price. Also the weighing stones used by him weigh only 90% of the correct weight. Find his effective percentage of mark-up.   (2 Marks )

A)  15%

B)  16^2/3%

C)  14^1/2%

D)  20%

Solution:- let the cost price be 100 of 1 kg....now he will sell 1 kg in 105 but due to error in weighing stones he will sell only 900 gram in 105 but he has paid 900*(100/1000)=90 rs for 900 grams. net profit=105-90=15 Rs...
percentage=100*(15/90)=16^2/3

13. Two merchants sell an article each for Rs.1000.one of them computes profit as a % of cost price, while the second calculates it incorrectly as a % of selling price. If both of them claim to have made a profit of 10%, who made more profit and by what amount? (1 Mark)

A) second and 9 rs

B) second and 10 rs

C)first and 9 rs

D)first and 10 rs

Solution:- first merchant get profit of 10% from cp=> (cp*110/100)=1000 => cp=Rs.909
so first merchant get profit of Rs.91.
second merchant get profit of 10% from sp=> profit=1000*10/100 =Rs.100
so the profit of second merchant is high and it is more than first merchant by 9Rs.