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 Profit and Loss Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  PROFIT  AND  LOSS  QUESTIONS

 

 

Selling Price (SP) : The price at which the shopkeeper sells the goods is called the selling price (SP) of the goods sold by the shopkeeper.

 

Profit : If the selling price of an article is more than its cost price, then the dealer (or shopkeeper) makes a profit (or gain)

i.e Profit = SP - CP;       SP > CP

 

Loss : If the selling price of an article is less than its cost price, then the dealer suffers a loss.

i.e loss = CP - SP;        CP > SP

 

IMPORTANT FORMULAE


1. Profit percentage = ProfitC.P×100

 

2. Loss percentage = LossC.P×100

 

3.S.P=100+Gain %100×C.P = 100-Loss%100×C.P

 

4. C.P=100100+Gain %×S.P = 100100-Loss %×S.P 

5. If an article is sold at a gain of say 35%, then SP = 135% of CP

6. If an article is sold at a loss of say 35%, then SP = 65% of CP

7. 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 :Loss % =Common Loss and Gain %10 2=x102

 

8. If a trader Professes to sell his goods at cost price, but uses false weihts, then 

Gain % =ErrorTrue Value - Error×100%

Q:

Every year before the festive season,a shopkeeper increases the price of the product by 35% and then introduce two successive discount of 10% and 15% respectively.what is percentage loss and percentage gain ?

A) 3.27 % loss B) 4.15 % loss
C) 3.27 % gain D) 4.15 % gain
 
Answer & Explanation Answer: C) 3.27 % gain

Explanation:

Let cp= 100,
35 % increase in sp=135
10 % discount in 135((135*10)/100)=13.5
so 1st sp=(135-13.5)=121.5, again 15 % discount in 1st sp((121.5*15)/100)=18.225
2nd sp=(121.5-18.225)=103.275,

so finally cp=100,sp=103.275 ,gain by 3.27%

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50 29721
Q:

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

A) 15 B) 16
C) 18 D) 25
 
Answer & Explanation Answer: B) 16

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x. 

S.P. of x articles = Rs. 20. 

Profit = Rs. (20 - x). 

20-xx*100=25 

=> 2000 - 100x = 25x 

=> 125x=2000 

=> x=16

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419 29709
Q:

On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is ?

A) Rs. 55 B) Rs. 60
C) Rs. 65 D) Rs. 70
 
Answer & Explanation Answer: B) Rs. 60

Explanation:

Let the cost price of a ball is Rs.x
Given, on selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls
The equation is :
17x - 720 = 5x
Solving the equation
we get x = 60
Therefore, cost price of a ball is Rs. 60.

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36 28998
Q:

'A' sold an article to 'B' at a profit of 20%. 'B' sold the same article to 'C' at a loss of 25% and 'C' sold the same article to 'D' at a profit of 40%. If 'D' paid Rs 252 for the article, then find how much did 'A' pay for it?

A) Rs.196 B) Rs.210
C) Rs.200 D) Rs.235
 
Answer & Explanation Answer: C) Rs.200

Explanation:

Let the article costs 'X' to A
Cost price of B = 1.2X
Cost price of C = 0.75(1.2X) = 0.9X
Cost price of D = 1.4(0.9X) = 1.26X = 252
Amount paid by A for the article = Rs. 200.

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46 28627
Q:

The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is :

A) Rs. 560 B) Rs. 530
C) Rs. 500 D) Rs. 514
 
Answer & Explanation Answer: C) Rs. 500

Explanation:

110% of S.P. = Rs. 616

S.P. = (616 x 100)/110 = Rs. 560

C.P = (110 x 560)/112 = Rs. 500

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64 28115
Q:

If goods be purchased for Rs.450 and 1/3 is sold at a loss of 10%. At what gain % should the remainder is sold to has to gain 20% on the whole transaction?

A) 35% B) 28%
C) 22% D) 19%
 
Answer & Explanation Answer: A) 35%

Explanation:

Given the cost price of the articles = Rs. 450

To get overall 20% gain,

Total Selling Price = (20/100) x 450 = 540


One third of the CP = 1/3 x 450 = Rs. 150

But given 1/3 of articles are sold at 10% loss

S.P of 1/3 of articles = 90% of 150

= 90 x 150/100 = 135

 

Then, S.P on remaining 2/3 goods must be

= 450 - 135 = 405 ...........(1)

CP on remaining goods

= 2/3 x 450 = 300 ............(2)


Profit = SP - CP = 405 - 300 = 105


Profit %  = (105/300) x 100

= 35%.

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45 27489
Q:

A dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was:

A) 10% loss B) 1% loss
C) 1% gain D) Neither loss nor profit
 
Answer & Explanation Answer: B) 1% loss

Explanation:

Loss%= (common gain or loss % / 10)2 = (10/10)² % = 1%.

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56 27321
Q:

A shopkeeper sells one-third of his goods at a profit of 10%, another one-third at a profit of 20%, and the rest at a loss of 6%.What is his overall profit percentage ?

A) 6% B) 8%
C) 10% D) 12%
 
Answer & Explanation Answer: B) 8%

Explanation:

Let the shopkeeper buy 300g for Rs.300. Now he sells 100g for Rs.110, another 100g for Rs120, and the rest 100g for Rs94. 

 

Therefore, the total amount he receives = Rs.110 + Rs.120 + Rs.94 = 324. 

 

Therefore, the shopkeeper spends Rs.300 and gets back Rs.324.

 

Therefore, his profit percentage = 24300x100 % = 8%

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