At what percentage above the CP must an article be marked to gain 20% after giving a discount of 20

Chapter 7: PROFIT AND LOSS

Introduction

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

• Direct Costs or Variable Costs : This is the cost associated with direct selling of product/service. In other words, this is the cost that varies with every unit of the product sold. Hence, if the variable cost in selling a pen for ` 20 is ` 5, then the variable cost for selling 10 units of the same pen is 10 × 5 = Rs. 50.




• Indirect Costs (Overhead Costs) or Fixed Costs : There are some types of costs that have to be incurred irrespective of the number of items sold and are called as fixed or indirect costs. For example, irrespective of the number of units of a product sold, the rent of the corporate office is fixed. Now, whether the company sells 10 units or 100 units, this rent is fixed and is hence a fixed cost.




• Apportionment of indirect (or fixed) costs : Fixed Costs are apportioned equally among each unit of the product sold. Thus, if n units of a product is sold, then the fixed cost to be apportioned to each unit sold is given by : \( \frac{\text{Fixed cost}}{n} \)




• The Concept of the Break-even Point : The break-even point is defined as the volume of sale at which there is no profit or no loss. In other words, the sales value in terms of the number of units sold at which the company breaks even is called the break-even point. This point is also called the break-even sales.




• Since for every unit of the product the contribution goes towards recovering the fixed costs, as soon as a company sells more than the break-even sales, the company starts earning a profit. Conversely, when the sales value in terms of the number of units is below the break-even sales, the company makes losses. The entire scenario is best described through the following example.

Q. Let us suppose that a paan shop has to pay a rent of ` 1000 per month and salaries of ` 4000 to the assistants. Also suppose that this paan shop sells only one variety of paan for ` 5 each

• The direct cost (variable cost) in making one paan is ` 2.50 per paan, then the margin is ` (5 – 2.50) = ` 2.50 per paan.




• Now, break-even sales will be given by: Break-even-sales = Fixed costs/Margin per unit = 5000/2.5 = 2000 paans




• Hence, the paan shop breaks-even on a monthly basis by selling 2000 paans

• Selling every additional paan after the 2000th paan goes towards increasing the profit of the shop. Also, in the case of the shop incurring a loss, the number of paans that are left to be sold to break-even will determine the quantum of the loss




• Profit = (Actual sales – Break-even sales) × Contribution per unit




• Loss = (Break-even sales – Actual sales) × Contribution per unit




• Profit Calculation on the Basis of Equating the Amount Spent and the Amount Earned




• A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his percentage profit.




• Since the money spent is equal to the money earned the percentage profit is given by




• % Profit = \( \frac{\text{Goods left}}{\text{Goods sold}} * 100\) = 5* 100/20 = 25%

IF THE TRADER PROFESSES TO SELL HIS GOODS AT COST PRICE BUT USES FALSE WEIGHTS,THEN

• GAIN= \( \frac{\text{ERROR}}{\text{(TRUE VALUE)-(ERROR)}} * 100 \)%

Q. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight . Find his gain percent.

• GAIN= \( \frac{\text{ERROR}}{\text{(TRUE VALUE)-(ERROR)}} * 100 \)%




• \( \frac{40}{960} * 100 \)%




• 4 1/6 %

Q.

A shopkeeper sold goods for ` 2000 at a profit of 50%. Find the cost price for the shopkeeper.

1500

1200

1333

1600

Ans .

1333 

1. Explanation :

   The shopkeeper sells his items at a profit of 50%. This means that the selling price is 150% of
   cost price (Since CP + % Profit = SP)
   For short you should view this as SP = 1.5 CP.

Q.

A man buys a shirt and a trousers for ` 371. If the trouser costs 12% more than the shirt, find the cost of the shirt.

125

150

175

200

Ans .

175 

1. Explanation :

   Let s = cost of a shirt
   If s = 150, 1.12s will be got by increasing s by 12% i.e. 12% of 150 = 18. Hence the value of 1.12s = 150
   + 18 =168 and s + 1.12s = 318 is not equal to 371. Hence check the next higher option.
   If s = 175, 1.12s = s + 12% of s = 175 + 21 = 196. i.e. 2.12 s = 371.
   Hence, Option (c) is correct.

Q.

A shopkeeper sells two items at the same price. If he sells one of them at a profit of 10% and the other at a loss of 10%, find the percentage profit/loss

2

1

0

3

Ans .

1 

1. Explanation :

   A shopkeeper sells two items at the same price. If he sells one of them at a profit of
   x% and the other at a loss of x%, find the percentage profit/loss. The result will always be a loss of [x/10]^2%. Hence, the answer here is [10/10]^2% = 1% loss.
   

Q.

If by selling 2 items for ` 180 each the shopkeeper gains 20% on one and loses 20% on the other, find the value of the loss

10

8

15

12

Ans .

15 

1. Explanation :

   The percentage loss in this case will always be (20/10)^2 = 4% loss.
   We can see this directly as 360 Æ 96% of the CP Æ CP = 360/0.96. Hence, by percentage change graphic
   360 has to be increased by 4.166 per cent = 360 + 4.166% of 360 = 360 + 14.4 + 0.6 = ` 375.
   Hence, the loss is ` 15.

Q.

By selling 15 mangoes, a fruit vendor recovers the cost price of 20 mangoes. Find the profit percentage.

33.33

36.33

37.33

45.33

Ans .

33.33 

1. Explanation :

   Here since the expenditure and the revenue are equated, we can use percentage profit = (goods left × 100)/goods sold = 5 × 100/15 = 33.33%

Q.

A dishonest shopkeeper uses a 900 gram weight instead of 1 kilogram weight. Find his profit percent if he sells per kilogram at the same price as he buys a kilogram

12.11

22.11

11.11

33.11

Ans .

11.11 

1. Explanation :

   Here again the money spent and the money got are equal. Hence, the percentage profit is got by goods left × 100/goods sold. This gives us 11.11%.
   

Q.

A manufacturer makes a profit of 15% by selling a colour TV for ` 6900. If the cost of manufacturing increases by 30% and the price paid by the retailer is increased by 20%, find the profit percent made by the manufacturer

9.15

7.15

6.15

8.15

Ans .

6.15 

1. Explanation :

   For this problem, the first line gives us that the cost price of the TV for the manufacturer is `6000. Further, if you have got to the 6000 figure by the end of the first line, reading further you can increase this
   advantage by calculating while reading as follows:
   Manufacturing cost increase by 30% so New manufacturing cost = 7800 and new selling price is 6900 + 20% of 6900 = 6900 + 1380 = 8280.
   Hence, profit = 8280 – 7800 = 480 and profit percent = 480 × 100/7800 = 6.15%
   

Q.

Find a single discount to equal three consecutive discounts of 10%, 12% and 5%

34.76

44.76

14.76

24.76

Ans .

24.76 

1. Explanation :

   Using percentage change graphic starting from 100: we get 100 Æ 88 Æ 83.6 Æ 75.24 (Note we can change percentages in any order).
   Hence, the single discount is 24.76%

Q.

A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol.

7

6

4

5

Ans .

4 

1. Explanation :

   10% reduction in price Æ 11.11% increase in consumption.
   But 11.11% increase in consumption is equal to 5 gallons. Hence, original consumption is equal to 45
   gallons for $180. Hence, original price = 4$ per gallon.

Q.

Ashok bought an article and spent ` 110 on its repairs. He then sold it to Bhushan at a profit of 20%. Bhushan sold it to Charan at a loss of 10%. Charan finally sold it for ` 1188 at a profit of 10%. How much did Ashok pay for the article.

890

1000

780

840

Ans .

780 

1. Explanation :

   Solve through options using percentage rule and keep checking options as you read. Try to finish the first option-check before you finish reading the question for the first time. Also, as a thumb rule
   always start with the middle most convenient option. This way you are likely to be required lesser
   number of options, on an average.

Q.

A dishonest businessman professes to sell his articles at cost price but he uses false weights with which he cheats by 10% while buying and by 10% while selling. Find his percentage profit

11.22

33.33

22.22

10

Ans .

22.22 

1. Explanation :

   Assume that the businessman buys and sells 1 kg of items. While buying he cheats by 10%,
   which means that when he buys 1 kg he actually takes 1100 grams. Similarly, he cheats by 10% while
   selling, that is, he gives only 900 grams when he sells a kilogram. Also, it must be understood that since
   he purportedly buys and sells the same amount of goods and he is trading at the same price while buying
   and selling, money is already equated in this case. Hence, we can directly use: % Profit = (Goods left ×
   100/Goods sold) = 200 × 100/900 = 22.22%

Q.

By selling 5 articles for ` 15, a man makes a profit of 20%. Find his gain or loss percentage if he sells 8 articles for ` 18.4

6

5

10

8

Ans .

8 

1. Explanation :

   By selling 5 articles for ` 15, a man makes a profit of 20% so SP = 3. Hence, CP = 2.5, if he sells 8 articles for ` 18.4 so SP = 2.3. Hence percentage loss = 8%.

Q.

Oranges are bought at 12 for a rupee and are sold at 10 for a rupee. Find the percentage profit or loss.

10

5

30

20

Ans .

10 

1. Explanation :

   Since money spent and got are equated, use the formula for profit calculation in terms of goods left/goods sold.
   This will give you percentage profit = 2/10 = 20%.
   Alternatively, you can also equate the goods and calculate the percentage profit on the basis of money as
   CP of 1 orange = 8.33 paise
   SP of 1 orange = 10 paise
   8.33 paise so 10 paise

Q.

A shopkeeper allows a rebate of 25% to the buyer. He sells only smuggled goods and as a bribe, he pays 10% of the cost of the article. If his cost price is ` 2500, then find what should be the marked price if he desires to make a profit of 9.09%

3500

4000

3000

2750

Ans .

4000 

1. Explanation :

   Use solving-while-reading as follows: Cost price (= 2500) + Bribe (= 10% of cost of article =
   250) = Total cost to the shopkeeper (2500 + 250 = 2750).
   He wants a profit of 9.09 percent on this value so Using fraction to percentage change table we get 2750
   + 9.09% of 2750 = 2750 + 250 = ` 3000. But this ` 3000 is got after a rebate of 25%. Since we do not have the value of the marked price on which 25% rebate is to be calculated, it would be a good idea to work reverse through the percentage change
   graphic: Going from the marked price to ` 3000 requires a 25% rebate. Hence the reverse process will be got by
   increasing ` 3000 by 33.33% and getting ` 4000

Q.

A man sells three articles, one at a loss of 10%, another at a profit of 20% and the third one at a loss of 25%. If the selling price of all the three is the same, find by how much percent is their average CP lower than or higher than their SP

8.25

7

10

9.2566

Ans .

9.2566 

1. Explanation :

   We have to calculate: (average CP – average SP)/average SP.
   Here, the selling price is equal in all three cases. Since the maximum number of calculations are
   associated with the SP, we assume it to be 100. This gives us an average SP of 100 for the three articles.
   Then, the first article will be sold at 111.11, the second at 83.33 and the third at 133.33. (The student is
   advised to be fluent at these calculations) Further, the CP of the three articles is 111.11 + 83.33 + 133.33
   = 327.77. The average CP of the three articles is 327.77/3 = 109.2566.
   Hence, (average CP – average SP)/average SP = 9.2566%. higher

Q.

A dishonest dealer professes to sell at cost price but uses a 900 gram weight instead of a 1 kilogram weight. Find the percent profit to the dealer

10

11.11

12.5

none

Ans .

11.11 

1. Explanation :

   Profit percent = (100/900) × 100 = 11.11%

Q.

By selling a watch for ` 495, a shopkeeper incurs a loss of 10%. Find the cost price of the watch for the shopkeeper.

545

550

555

565

Ans .

550 

1. Explanation :

   0.9 × Price = 495 so Price 550

Q.

By selling a cap for Rs 34.40, a man gains 7.5%. What will be the CP of the cap?

32.8

32

32.4

28.8

Ans .

32 

1. Explanation :

   The SP = 107.5% of the CP. Thus, CP = 34.4/1.075 = ` 32.

Q.

A cellular phone when sold for ` 4600 fetches a profit of 15%. Find the cost price of the cellular phone

4300

4150

4000

4500

Ans .

4000 

1. Explanation :

   1.15 × Price = 4600 so Price = 4000

Q.

A machine costs ` 375. If it is sold at a loss of 20%, what will be its cost price as a percentage of its selling price?

80

120

110

125

Ans .

125 

1. Explanation :

   A loss of 20% means a cost price of 100 corresponding to a selling price of 80. CP as a percentage of the SP would then be 125%

Q.

A shopkeeper sold goods for ` 2400 and made a profit of 25% in the process. Find his profit percent if he had sold his goods for ` 2040.

6.25

7

6.2

6.5

Ans .

6.25 

1. Explanation :

   2400 = 1.25 × cost price Æ Cost price = 1920
   Profit at 2040 = ` 120
   Percentage profit = (120/2040) × 100 = 6.25%

Q.

A digital diary is sold for ` 935 at a profit of 10%. What would have been the actual profit or loss on it, if it had been sold for ` 810?

45

40

48

50

Ans .

40 

1. Explanation :

   CP = 935/1.1 = 850. Selling this at 810 would mean a loss of `40 on a CP of ` 850

Q.

A music system when sold for ` 4500 gives a loss of 16.66% to the merchant who sells it. Calculate his loss or gain per cent, if he sells it for ` 5703.75

Loss of 5.625%

Profit of 8.33%

Loss of 7%

Profit of 5.625%

Ans .

5.625 

1. Explanation :

   The CP will be ` 5400. Hence at an S.P. of 5703.75 the percentage profit will be 5.625%

Q.

By selling bouquets for ` 63, a florist gains 5%. At what price should he sell the bouquets to gain 10% on the cost price?

66

69

72

72.5

Ans .

66 

1. Explanation :

   CP = 63/1.05 = 60. Thus, the required SP for 10% profit = 1.1 × 60 = 66

Q.

A shopkeeper bought 240 chocolates at ` 9 per dozen. If he sold all of them at Re. 1 each, what was his profit per cent?

66(1/6)%

33(1/3)

24%

27%

Ans .

33.33 

1. Explanation :

   The buying price is ` 9 per dozen, while the sales price is ` 12 per dozen – a profit of 33.33%

Q.

A feeding bottle is sold for ` 120. Sales tax accounts for one-fifth of this and profit one-third of the remainder. Find the cost price of the feeding bottle.

64

72

68

76

Ans .

64 

1. Explanation :

   Sales tax = 120/5 =24. Thus, the SP contains ` 24 component of sales tax. Of the remainder (120 – 24 = 96) 1/3rd is the profit. Thus, the profit = 96/3 = 32. Cost price = 96 – 32 = 64

Q.

Find a single discount equivalent to the discount series of 20%, 10%, 5%.

30%

31.6%

68.4%

35%

Ans .

31.6%  

1. Explanation :

   100 becomes 80 (after 20% discount) becomes 72 (after 10% discount) becomes 68.4 (after 5% discount). Thus, the single discount which would be equivalent would be 31.6%

Q.

A coal merchant makes a profit of 20% by selling coal at ` 25 per quintal. If he sells the coal at ` 22.50 per quintal, what is his profit per cent on the whole investment?

6

6.66

7.5

8

Ans .

8 

1. Explanation :

   C.P × 1.2 = 25 Æ CP = 20.833
   At a selling price of ` 22.5, the profit percent 1.666/20.833 = 8%

Q.

The cost price of a shirt and a pair of trousers is ` 371. If the shirt costs 12% more than the trousers, find the cost price of the trouser

125

150

175

200

Ans .

175 

1. Explanation :

   Solve using options. Option (c) gives you ` 175 as the cost of the trouser. Hence, the shirt will cost 12% more i.e. 175 + 17.5 + 3.5 = 196.
   This satisfies the total cost requirement of ` 371

Q.

A pet shop owner sells two puppies at the same price. On one he makes a profit of 20% and on the other he suffers a loss of 20%. Find his loss or gain per cent on the whole transaction.

Gain of 4%

No profit no loss

Loss of 10%

Loss of 4%

Ans .

Loss of 4% 

1. Explanation :

   The formula that satisfies this condition is:
   Loss of a2/100% (Where a is the common profit and loss percentage). Hence, in this case 400/100
   = 4% loss.

Q.

The marked price of a table is ` 1200, which is 20% above the cost price. It is sold at a discount of 10% on the marked price. Find the profit per cent

10

8

7.5

6

Ans .

8 

1. Explanation :

   If marked price is 1200, then CP is 1000.  and the selling price is 1080. which means profit of (1080-1000)/1000 = 8%

Q.

125 toffees cost ` 75. Find the cost of one million toffees if there is a discount of 40% on the selling price for this quantity.

3,00,000

3,20,000

3,60,000

4,00,000

Ans .

360000 

1. Explanation :

   The cost per toffee = 75/125= ` 0.6 = 60 paise. Cost of 1 million toffees = 600000. But there is a discount of 40% offered on this quantity. Thus, the total cost for 1 million toffees is 60% of
   600000 = 360000.

Q.

A shopkeeper marks the price of an article at ` 80. Find the cost price if after allowing a discount of 10% he still gains 20% on the cost price

53.33

70

75

60

Ans .

60 

1. Explanation :

   On a marked price of ` 80, a discount of 10% would mean a selling price of ` 72. Since this represents a 20% profit we get:
   1.2 × CP = 72 so CP = 60

Q.

The printed price of a calculator is ` 180. A retailer pays ` 137.7 for it by getting successive discounts of 10% and another rate which is illegible. What is the second discount rate?

12%

12.5%

15%

20%

Ans .

15%  

1. Explanation :

   180 × 0.9 × x = 137.7 becomes x = 0.85
   Which means a 15% discount

Q.

How much percent more than the cost price should a shopkeeper mark his goods, so that after allowing a discount of 12.5% he should have a gain of 5% on his outlay?

9.375

16.66

20%

25%

Ans .

 20% 

1. Explanation :

   If you assume the cost price to be 100 and we check from the options, we will see that for Option (c) the marked price will be 120 and giving a discount of 12.5% would leave the shopkeeper with
   a 5% profit

Q.

A dishonest dealer professes to sell at cost price but uses a 900 gram weight instead of a 1 kilogram weight. Find the percent profit to the dealer.

10%

11.11%

12.5%

None of these

Ans .

11.11 

1. Explanation :

   Profit percent = (100/900) × 100 = 11.11%

Q.

A trader purchases apples at ` 60 per hundred. He spends 15% on the transportation. What should be the selling price per 100 to earn a profit of 20%?

72

81.8

82.8

83.8

Ans .

82.8 

1. Explanation :

   Cost per 100 apples = 60 + 15% of 60 = ` 69.
   Selling price @ 20% profit = 1.2 × 69 = ` 82.8

Q.

a milkman sells his buffalo for ` 720 at some profit. Had he sold his buffalo at ` 510, the quantum of the loss incurred would have been double that of the profit earned. What is the cost price?

600

625

675

none

Ans .

none

1. Explanation :

   A cost price of ` 650 would meet the conditions in the problem as it would give us a loss of 140 (if sold at 510) and a profit of 70 (when sold at 720)

Q.

A shopkeeper buys an article for ` 400 and marks it for sale at a price that gives him 80% profit on his cost. He, however, gives a 15% discount on the marked price to his customer. Calculate the actual percentage profit made by the shopkeeper.

62

64

54

53

Ans .

53 

1. Explanation :

   If the cost price is 100, a mark up of 80% means a marked price of 180. Further a 15% discount on the marked price would be given by:
   180 – 15% of 180 = 180 – 27 =153. Thus, the percentage profit is 53%

Q.

A watch dealer pays 10% custom duty on a watch that costs ` 250 abroad. For how much should he mark it, if he desires to make a profit of 20% after giving a discount of 25% to the buyer?

400

440

275

330

Ans .

440 

1. Explanation :

   Cost price to the watch dealer
   = 250 + 10% of 250 = ` 275
   Desired selling price for 20% profit
   = 1.2 × 275 = 330
   But 330 is the price after 25% discount on the marked price.
   Thus,
   Marked price × 0.75 = 330 so MP = 440
   Hence, he should mark the item at ` 440.

Q.

A man buys 50 kg of oil at ` 10 per kilogram and another 40 kg of oil at ` 12 kilogram and mixes them. He sells the mixture at the rate of ` 11 per kilogram. What will be his gain percent if he is able to sell the whole lot?

100/98

100 10/49

10 1/49

none

Ans .

100/98 

1. Explanation :

   Total cost = 50 × 10 + 40 × 12 = 980. Total revenue = 90 × 11 = 990. Gain percent = (10 × 100)/980 = 100/98 %.

Q.

If the cost price of 30 articles is equal to the selling price of 20 articles, find the profit percent

33.33

40

50

60

Ans .

50 

1. Explanation :

   goods left/Goods sold * 100 = = 10/20 × 100 = 50%

Q.

A shopkeeper sells sugar in such a way that the selling price of 950 gm is the same as the cost price of one kilogram. Find his gain percent.

100/17

150/17

5 (5/19)

1/19

Ans .

5 (5/19) 

1. Explanation :

   The profit percent would be equal to 50 × 100 /950 = 5000/950 = 100/19% = 5 (5/19)%

Q.

A sold a table to B at a profit of 20%. B sold the same table to C for ` 75 thereby making a profit of 25%. Find the price at which A bought the table from X if it is known that X gained 25% in the transaction

30

40

50

60

Ans .

50 

1. Explanation :

   B sold the table at 25% profit at ` 75. Thus cost price would be given by: CPB × 1.25 = 75
   B’s Cost price = ` 60.
   We also know that A sold it to B at 20% profit.
   Thus,
   A’s Cost price × 1.2 = 60
   so A’s cost price = 50.

Q.

A sold a table to B at a profit of 15%. Later on, B sold it back to A at a profit of 20%, thereby gaining ` 69. How much did A pay for the table originally?

300

320

345

350

Ans .

300 

1. Explanation :

   300 (A buys at this value) Æ 345 (sells it to B at a profit of 15%) Æ 404 (B sells it back to A at a profit of 20% gaining ` 69 in the process). Thus, A’s original cost = `300

Q.

A colour TV and a VCP were sold for ` 12,000 each. The TV was sold at a loss of 20% whereas the VCP was sold at a gain of 20%. Find gain or loss in the whole transaction

1200 loss

1000 loss

960 loss

1040 loss

Ans .

1000 

1. Explanation :

   The CP of the TV Æ CPTV × 0.8 =12000 Æ CPTV = 15000
   The CP of the VCP Æ CPVCP × 1.2 = 12000 so CPVCP = 10000.
   Total sales value = 12000 × 2 = 24000.
   Total cost price = 15000 + 10000 = 25000. Loss = 25000 – 24000= 1000

Q.

The cost of manufacturing an article is made up of materials, labour and overheads in the ratio 4 : 3 : 2. If the cost of labour is ` 45, find the profit percent if the article is sold for ` 180

50

33.33

25

20

Ans .

33.33 

1. Explanation :

   The total manufacturing cost of the article = 60 + 45 + 30 = 135. SP = 180. Thus, profit = ` 45. Profit Percent = 45 × 100/135 = 33.33%

Q.

Two dealers X and Y selling the same model of refrigerator mark them under the same selling prices. X gives successive discounts of 25% and 5% and Y gives successive discounts of 16% and 12%. From whom is it more profitable to purchase the refrigerator?

From Y

From X

Indifferent between the two

Cannot be determined

Ans .

From X 

1. Explanation :

   Assume marked price for both to be 100.
   X’s selling price = 100 × 0.75 × 0.95 = 71.25
   Y’s selling price = 100 × 0.84 × 0.88 = 73.92.
   Buying from ‘X’ is more profitable

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

Quiz

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