July 3, 2013

Profit and Loss

Concept test
Topic: Profit and Loss
1. P sold an article for Rs.1080 thereby losing 10% Q sold another article for Rs.1800 at a loss

of 10%. Who incurred a greater loss?

a)P b) Q c) Cannot say d) Both have equal

Solution: For P, SP=1080 and loss=10% => CP = 1080/0.9 =1200 => loss = 1200-1080 = 120. For Q, SP=1800 and loss=10% => CP = 1800/0.9 = 2000 => loss = 2000-1800 = 200.

2. Jawed sells 2,000 mangoes in a week. He recovers his total cost by selling first 1,200 Mangoes. He sells the next 300 Mangoes for a loss of 20% and he sells the last 500 Mangoes for a loss of 40%. What is his overall percentage of profit?

a)45% b) 35% c) 27% d) 12.5%

Solution :300 sold at loss of 20% and 500 old at a loss of 40% => loss% = (3/8)X20 + (5/8)X40 = 32.5 => loss factor = 0.675 Already he got a gain by SP of 1200 = CP of 2000. So overall profit % = (2000/1200) X 0.675 = 1.125 => 12.5% gain.

3. A trader purchases two watches. He marks the first one up by Rs.200 over the cost price and gives a discount of 20% on it. The second one he marks up by 50% and gives a discount of Rs.160. If he gains 15% on both the watches put together and 8% on the first alone, what is the percentage of profit on the second watch?

a)21% b) 22% c) 18.5% d) Can’t be determined

Solution :MP1 = CP1 + 200 and discount = 20%.Also MP2 = 1.5CP2 and discount = Rs. 160. Also SP1/CP1 = 8% gain. With this information it can’t be said what is the profit % on
2nd watch

4. The marked prices of two articles are in the ratio of 1:2, their discount percentages are also in the ratio of 1:2 and the profit they get is also in the ratio of 1:2. What is the ratio of their cost price

a)1:2 b) 5:8 c) 2:5 d) Can’t be determined

Solution: Without the knowledge of at least one of the prices the ratio of CP’s can’t be determined

5. The cost price of a computer is Rs.1000 less then the selling price of a television and the selling price of the computer is 30% more than the cost price of the television. If the selling price of the computer is 4% more than the selling price of the television, what is the percentage of profit on selling the television?

a)20% b) 25% c) 162/3% d) Can’t be determined.

Solution: CP computer = SP TV – 1000 and SP computer = 1.3 X CP TV. SP Computer =SP TV => 1.3 CP TV = 1.04 SP TV => SP/CP = 1.25 => 25% gain.

6. A trader buys 150 pens for Rs.1000 and he marks each of them at Rs.10. He gives a discount of 20% on each pen and he gives 1 pen free on bulk purchases of 9 pens. What is his minimum possible overall percentage of profit?

a)8% b) 10% c) 20% d) 5%

Solution : 150 pens for Rs.1000 => total CP = 1000. 1 pen free for every 9 pens => he can sell 135 pens (for least possible profit) SP of each pen = 10 and discount = 20% => SP = 8. Total SP = 135 X 8 = 1080 => SP/CP = 1080/1000 = 1.08 => 8%.

7. A fruit vendor sells mangoes and bananas and gets equal revenue from each. He gets a profit of 20% on each mango and a profit of 25% on each banana. If the ratio of the number of bananas sold to the number of mangoes sold is 4:1, what is the ratio of the cost price of a banana to that of a mango?
a)1:5 b) 6:25 c) 2:9 d) Can’t be determined

Solution :For mango, SP = 1.2 CPm and for banana SP = 1.25 CPb. Revenue from mango = revenue from banana => 1.2 CPm = 4 X 1.25 CPb (since they are sold in ratio of 1:4) So, CPb/CPm = 6:25.

8. A dishonest oil merchant claims that he gets a profit of only 5% but he gives only one liter of oil instead of 1kg. If 1.25 liter of oil weighs 1kg what is his overall percentage of profit

a)31.25% b) 25% c) 26% d) None of these

Solution :Overall profit = 1.05 X (1.25/1) = 1.3125 => 31.25% gain

9. The percentage by which the marked price exceeds the cost price of an article and the percentage of discount allowed on the article are in the ratio of 3:2. If it is sold at the cost price, what is the percentage of discount allowed?

a)20% b) 25% c) 331/3% d) 50%

Solution :If CP is raised by 3x %, the discount should be 2x %. Also, after discount SP=CP => increase of 3x% X decrease of 2x%. From inspection, 33.33% discount => 50% increase (since 3:2) and 1.5 X 0.6666 = 1.

10. A merchant professed to sell 20 articles at a loss which is equals to the cost price of 2 articles but sold 18 articles at the cost price of 20 articles. What is the gain percent?

1) 191/11% 2) 10% 3) 111/9% 4) 0%

Solution :SP of 18 articles = CP of 20 articles => SP/CP = 20/18 = 1.1111 => 11.11% gain

11. The cost of an apple is 331/3% less than the cost of 1 mango. If a man sells four apples at the cost price of 5 mangoes, what is his percentage of profit?

1) 75% 2) 81% 3) 87.5% 4) 90%

Solution :CP of apple = 0.6666 X CP of mango…….1 Man sold 4 apples for CP of 5 mangoes

i. his CP = 4 X CP of apple And his SP = 5 X CP of mango. So, SP/CP = (5XCP of mango)/(4XCP of apple) = 1.875 => 87.5%.

12. The catalogue price of an article is Rs.15000. If the discount is increased from 15% to 20%, then profit falls from 27.5% to 20%. Find the cost price of the article?

1) Rs.12000 2) Rs.10000 3) Rs.12250 4) Rs.1750

Solution :MP = 15000. 5% change in discount i.e., 5% of MP = 7.5 % of CP (profit change) So, CP = 5/7.5 X MP = 10000

13. 5kg of ghee was bought by Venu for Rs.300. One kg becomes spoilt. He sells the remaining in such a way that on the whole he incurs a loss of 10%. At what price per kg does he sell the ghee?

1) Rs.46.25 2) Rs.45.70 3) Rs.46.60 4) Rs.67.50

Solution :CP of 5 kg ghee = 300. Loss = 10% => SP = 0.9 CP = 270. For Rs. 270, 4 kg are sold SP for 1 kg = 270/4 =Rs. 67.5

14. A trader professes to lose 10% in selling 2kgs of rice. He uses 2 weighing stones, each of which is marked 1kg but weighs less. If the percentage of profit is 26/7% and one of the two stones weighs only 800 gm, how much does the second stone weigh

1) 800gm 2) 850gm 3) 900gm 4) 950gm

Solution :Let w be the weight of the second stone. Now, 0.9 X (1000/800) X (1000/w) = 1.0285 (since profit is 2.85%) w = 900 gm (nearly)
15. Ramya bought a certain number of apples at 6 apples for Rs.10 and sold them at 4 apples for Rs.10. Find the number of apples she bought if total gain is Rs.60

1) 30 2) 31 3) 62 4) None of these

Solution :CP => 6 apples for Rs. 10. SP => 4 apples for Rs. 10 => 6 apples for Rs. 15 So, for 6 apples, gain is Rs.5 => Rs. 60 gain requires 72 apples
16. A mechanic purchases a cooler for Rs.32000 and incurs Rs.13000 on installation and repairs. After one year he sold it for Rs.40000. What is the profit or loss percentage, if the deprecation rate of the machine is 20% per annum?

1) 81/3% 2) 121/12% 3) 161/4% 4) 111/9%

Solution :Total CP = 45000. Depreciation = 20% =>new CP = 0.8 X 45000 = 36000. SP = 40000 => SP/CP = 40/36 = 1.1111 => 11.11% gain

A trader offers to give two articles free for every 10 articles I purchase. I get a total of 10 articles free for my purchase and I sell them all at a rate such that I get back my investment from the sale of just 10 of the articles. What is my overall percentage of profit

1) 100% 2) 150% 3) 500% 4) 250%

Solution :2 articles free for every 10 articles bought. So 10 free articles => 50 articles bought. Money of 60 articles (10 articles free) is obtained by selling only 10 articles. So SP of 10 articles = CP of 60 articles => SP/CP = 6 => 500% gain

Due to a slump in the market, A, while selling 12 apples to B, allows him to count them as 9. But due to an overnight demand A is forced to buy them back at the same rate as he sold and allows B to count 9 apples as 12. What is overall gain percentage of B

1) 777/9% 2) 75% 3) 50% 4) 662/3%

Solution :In two transactions B is gaining => SP > CP for B in two transactions. So, gain% = 12/9 X 12/9 = 1.7777 => 77.77%.

Arun purchased a house for Rs.75000 and a site for Rs.15000 respectively, if he sold the house for Rs.83000 and the site for Rs.10000, then find the resultant percentage of gain?

1) 3% 2) 31/3% 3) 30% 4) 331/3%

Solution :Total CP = 90000 & total SP = 93000 => gain = SP/CP = 93000/90000 =1.0333 = 3.33%

A sells an article to B at a gain of 20%. B sells is to C at a gain of 25% and C in turn sells is to D at a loss of 331/3%. If D paid Rs.1000 for it, then what is the cost price of A.?
1) Rs.1000 2) Rs.2000 3) Rs.3000 4) Rs.4000

Solution :1.2 X 1.25 X 0.6666 X CP = 1000 => CP = 1000 (profits of 20%, 25% & loss of 33.33%)