Chapter 7: PROFIT AND LOSS


Introduction


Cost Price = cost of item
Selling price = price at which item is sold.
Gain = Selling price - Cost price (SP > CP)
Loss = Cost price - Selling price (CP > SP)

                          SP={(100+GAIN%) /100}*CP
                          SP={(100-LOSS%)/100}*CP
                     CP=100/(100+GAIN%)}*SP
                     CP=100/(100-LOSS%)}*SP

So when an article of Rs 100 is sold at 35% gain that means SP is Rs.135
So when an article of CP = 100 is sold for loss of 35% its SP is Rs. 65.

When a item is sold for x% gain and other for x% loss, the seller incurs a loss of 

                                      Loss = ( X / 10) ^ 2

Questions and Answers


Q. A person incurs loss of 5% by selling a watch for Rs 1140. At what price should the watch be sold to earn a  5% profit ?

A. CP is 100/95 * 1140 as a loss of 5% on CP is 1140 so CP is 100/95% of 1140 [SP] as per formula above.


New selling price = (100 / 95) * ( 105 / 100) * 1140 = 1260


Q. By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .

A.

Selling price of 33m - CP of 33 m = SP of 11m [Gain].

SP of 22 m = CP of 33m i.e. SP of 2 m = CP of 3 m

Assume CP of 1 m = Re. 1 so 3 m is Rs. 3.

SP of 2 m = Rs. 3 and SP of 1 m = Rs. 1.5 so gain is 50%.


Q. A man brought toffees at 3 for a rupee. How many for a rupee must he sell to gain 50%?

A. Cost of a toffee is 3 toffees is re. 1. So he needs to sell them at Rs. 1.5 to make a gain of 50% so at 50 paise each or 2 for a rupee.


Q. A  grocer  purchased  80  kg  of  sugar  at Rs.13.50  per  kg  and mixed  it with 120kg sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%?

A. The cost of the mixture

= (weight1 * price1) + (weight2*price2) / (weight1+weight2)

= (80*13.5) + (120*16) / (120+80)

=(1080+1920)/200 = 3000/200 = Rs. 15 / kg


SP = 116/100 * 15 = 1.16*15=17.4 Rs


Q. Pure ghee cost Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50 per kg,   A  shopkeeper  sells  the mixture at  the rate of Rs.96 per kg,  thereby making a profit of 20%. In What ratio does he mix the two?

A. SP of mixture = 96 ; CP of mixture = 80 as SP is 20% more than CP;


Rule of alligation:

(Quantity of oil : Quantity of ghee)

= ( CP of ghee - Mean price) / (Mean price - CP of oil)

= (100-80) / (80-50)

=20/30 = 2:3


Q. Monika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent.

A. Assume it was with a SP of Rs. 100 it was bought for Rs. 90 and sold for Rs. 108 thus making profit of Rs. 18 which is 20% more than Rs. 90.


Q. A  tradesman  sold  an  article  at  a  loss  of  20%. if  the  selling  price  has  been increased by Rs 100, there would have been a gain of 5%. what was the cost price of the article?

A. SP(old) = 80% of CP

SP(new) = 105% of CP; we know (105% of CP) - (80% of CP) = 100

i.e. 25% of CP = 100; Hence CP = Rs. 400


Q. A man sells an article at a profit of 25% if he had bought it 20% less and sold it for  Rs 10.50 less, he would have gained 30% find the cost price of the article.

A. SP1 = 1.25CP1 as it is sold for 25% profit. CP2 = (4/5)*CP1;

SP2 = (130/100)*CP2

SP2 = SP1 - 10.5 = 1.25CP1 - 10.5


so we get

1.25CP1 - 10.5 = (130/100)*(4/5)*CP1

1.25CP1 - 1.04CP1 = 10.5

0.21CP1 = 10.5

CP1 = Rs.50


Q. A dealer sold three-fourth of his article at a gain of 20% and remaining at a cost price. Find the gain earned by him at the two transaction.

A. assume he had 4 articles of CP = 100 so he sold three at 120 and 1 at 100. so he earned profit of Rs. 60. CP of total inventory is 400 so profit is 15%.


Q. A man bought a horse and a bull for Rs 3000.he sold the horse at a gain of 20% and the bull at a  loss of 10%,thereby gaining 2% on the whole. find the cost of the horse.

A. 1.2x + 0.9(3000-x) = 3600 is the equation as 'x' is price of horse. 1.2x is SP of horse at 20% profit and 0.9(3000-x) is SP of bull at 10% loss. rs 3600 is the SP of total transaction at 2% profit over Rs. 3000.


Q. find the single discount equivalent to a series discount of 20% ,10% and 5%

A. assume CP=100 so apply 20% discount to get CP=80 and then 10% to get 72 and then 5% to get 72-3.6 = 68.4 so total is 31.6%.


Q. A retailer marks all  its goods at 50% above  the cost price and thinking  that he will still make 25% profit,offers a discount of 25% on  the marked price.what is the actual profit on the sales?

A. Assume price is 100 so SP is 150 and 25% discount on SP gives new SP as Rs 112.5. So profit is 12.5%


Q. At what %  above C.P must  an  article be marked  so  as  to  gain  33%  after allowing a customer a discount of 5%?

A. We have to find the value of SP [assume as 'x'] whose 95% is 33% above CP. Assume CP to be Rs 100 and SP(new) will be Rs. 133.

0.95x = 133

x = 133 * 100 / 95 = 133 * 20 / 19 = 140


Q. A merchant sold his goods for Rs.75 at a profit percent equal to C.P. The C.P was :

A. SP = (100+Gain%) * CP /100 we get below equation by substituting these values

75 = ( 100 + x) * x / 100

Read and Answer

A certain perfume is available at a duty-free shop at the Bangkok international airport. It is priced in the Thai currency Baht but other currencies are also acceptable. In particular, the shop accepts Euro and US Dollar at the following rates of exchange:
US Dollar 1 = 41 Bahts
Euro 1= 46 Bahts
The perfume is priced at 520 Bahts per bottle. After one bottle is purchased, subsequent bottles are available at a discount of 30%. Three friends S, R and M together purchase three bottles of the perfume, agreeing to share the cost equally. R pays 2 Euros. M pays 4 Euros and 27 Thai Bahts and S pays the remaining amount in US Dollars


Q. How much does R owe to S in Thai Baht?


  1. 428

  2. 416

  3. 334

  4. 324


Ans . D


  1. S, M and R in all spend 1248 Bahts. Initially M pays 211 Bahts and R pays 92 Bahts. Remaining is paid by S i.e; 945 Bahts

  2. If 1248 is divided equally among S, M and R, each has to spend 415 Bahts.

  3. Hence, M has to pay 205 Bahts which is 5 Dollars to S. and R has to pay 324 Bahts to S.



Q. How much does M owe to S in US Dollars?


  1. 3

  2. 4

  3. 5

  4. 6


Ans . C


  1. S, M and R in all spend 1248 Bahts. Initially M pays 211 Bahts and R pays 92 Bahts. Remaining is paid by S i.e; 945 Bahts

  2. If 1248 is divided equally among S, M and R, each has to spend 415 Bahts.

  3. Hence, M has to pay 205 Bahts which is 5 Dollars to S. and R has to pay 324 Bahts to S.


CAT Problems


Q.A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?


  1. 9 : 1
  2. 10 : 1
  3. 11 : 1
  4. None of these

Ans.b


Q.A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?


  1. 100
  2. 80
  3. 75
  4. 66.66

Ans.a


Q.The rate of inflation was 1000%. Then what will be the cost of an article, which costs 6 units of currency now, 2 years from now?


  1. 666
  2. 660
  3. 720
  4. 726

Ans.d


Q.A man invests Rs.3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?


  1. 1200
  2. 1300
  3. 1500
  4. 2000

Ans.c


Q.I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%. What is the percentage of loss(–) or profit(+) that resulted from the transaction?


  1. 10

  2. -1

  3. 1

  4. 10


Ans.b


A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54.

Q.What is the actual price per piece?


  1. 82

  2. 41

  3. 6

  4. 28


Ans.b


Q.What is the actual quantity sold?


  1. 28

  2. 14

  3. 82

  4. 41


Ans.a


Q.A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100.If he is able to sell only 1,200 out of 1,500 watches he has made in the season, then he has made a profit of


  1. Rs. 90,000

  2. Rs. 75,000

  3. Rs. 45,000

  4. Rs. 60,000


Ans.b


Q.If he produces 1,500 watches, what is the number of watches that he must sell during the season in order to break-even, given that he is able to sell all the watches produced?


  1. 500

  2. 700

  3. 800

  4. 1000


Ans.b


Q.The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.


  1. 1.4 lakh

  2. 2 lakh

  3. 1 lakh

  4. 2.1 lakh


Ans.c


Q.After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?


  1. 28.56%

  2. 35%

  3. 22.22%

  4. None of these


Ans.a


Q.A dealer buys dry fruits at Rs. 100, Rs. 80 and Rs. 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight, and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit?


  1. 80

  2. 100

  3. 95

  4. none


Ans.d



 

Quiz

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