Profit and Loss Questions

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:

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 25675
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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50 24616
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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Q:

If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265

A) Rs. 750 B) Rs. 800
C) Rs. 850 D) Rs. 900
 
Answer & Explanation Answer: B) Rs. 800

Explanation:

Let the cost of Production = Rs. P

Then, as per question,

 

125100×115100×110100×P=1265

 

=> P=800

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71 23575
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 23404
Q:

A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was

A) Rs 100 B) Rs 150
C) Rs 200 D) Rs 250
 
Answer & Explanation Answer: C) Rs 200

Explanation:

Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price  = (95/100) * x  = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200

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102 23204
Q:

The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit ?

A) Rs. 660 B) Rs. 560
C) Rs. 1060 D) Rs. 960
 
Answer & Explanation Answer: D) Rs. 960

Explanation:

Let C.P. = Rs. C.
Then, 832 - C = C - 448
2C = 1280 => C = 640
Required S.P. = 150% of Rs. 640 = 150/100 x 640 = Rs. 960.

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Q:

The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of two selling prices is

A) 51:52 B) 52:53
C) 53:54 D) 54:55
 
Answer & Explanation Answer: B) 52:53

Explanation:

Let the Cost price of article is Rs. x

Required ratio = (104% of x) / (106% of x)

                            =104/106

                            =52/53 = 52:53                     

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