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 = 

2. Loss percentage = 

3. 

4. 

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 :

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

%

Q:

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

A) No profit, no loss B) 5%
C) 8% D) 10%
 
Answer & Explanation Answer: B) 5%

Explanation:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain ={\color{Black} \left ( \frac{80}{1600} \times 100\right ) }% = 5%

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162 25723
Q:

By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?

A) 16 B) 18
C) 20 D) 22
 
Answer & Explanation Answer: B) 18

Explanation:

Let S.P. of 45 lemons be Rs. x.

Then, 80 : 40 = 120 : x or   x = = 60

For Rs.60, lemons sold = 45

For Rs.24, lemons sold  == 18.

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176 24465
Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

A) 116% B) 166.66%
C) 60% D) 100%
 
Answer & Explanation Answer: B) 166.66%

Explanation:

Let the cost price of 1 litre pure milk be Re.1, then 

\inline \begin{Bmatrix} 6 & litres(milk) & \rightarrow & CP=Rs.6\\ 2 & litres(water) & \rightarrow & CP=Rs.0 \end{Bmatrix}\rightarrow CP=Rs.6 only

and 8 litre mixture  \rightarrow SP \rightarrow 8 x 2 = Rs.16

Profit %= %

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148 22349
Q:

A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.

A) 20% B) 21%
C) 22% D) 23%
 
Answer & Explanation Answer: B) 21%

Explanation:

Gain % = \inline \fn_jvn {\color{Black} (\frac{(100+common\; gain\; percent)^{2}}{100}-100)}%

            = \inline \fn_jvn {\color{Black} (\frac{(100+10)^{2}}{100}-100)}%

            = \inline \fn_jvn {\color{Black} (\frac{12100-10000}{100})}%

            = 21%

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93 20861
Q:

The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

A) Rs. 2000 B) Rs. 2200
C) Rs. 2400 D) Data inadequate
 
Answer & Explanation Answer: A) Rs. 2000

Explanation:

Let C.P. be Rs. x.

Then,{\color{Black} \Rightarrow }{\color{Black} \frac{1920-x}{x}\times 100=\frac{x-1280}{x}\times 100}

{\color{Black} \Rightarrow } 1920 - x = x - 1280

{\color{Black} \Rightarrow } 2x = 3200

{\color{Black} \Rightarrow } x = 1600

{\color{Black}\therefore } Required S.P. = 125% of Rs. 1600 ={\color{Black}Rs.\left ( \frac{125}{100}\times 1600 \right )=Rs 2000 }

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