Arithmetic - Profit & Loss - Previous Year CAT/MBA Questions
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Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is
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Answer:1000
Explanation :
Let the total number of pens Amal bought = x
Also, let the wage of the employee = w
∴ Amal’s total cost price = 8x + w
Total selling price of the first 100 pen = 100 × 12 = 1200
Case 1: The remaining pen when each is sold at Rs. 11
Total selling price of the remaining pen = (x - 100) × 11
⇒ 1200 + 11(x - 100) = 8x + w + 300
⇒ 3x - 200 = w …(1)
Case 2: The remaining pen when each is sold at Rs. 9
Total selling price of the remaining pen = (x - 100) × 9
⇒ 1200 + 9(x - 100) = 8x + w - 300
⇒ 4x - 600 = w …(2)
A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is
A.
692
B.
688
C.
675
D.
653
Answer: Option
B
Explanation :
Let 2, 3, 5 kgs is bought of each variety respectively.
∴ Total quantity bought = 2 + 3 + 5 = 10 kgs
Total cost of tea = 2 × 800 + 3 × 500 + 5 × 300 = 4600.
Profit on total quantity = 50%
∴ Total selling price for 10 kg tea = 4600 × 1.5 = 6900.
Selling price for 1/6th of 10 kg tea = 10/6 × 700 = 7000/6
⇒ Selling price for remaining 50/6 kg tea = 6900 – 7000/6 = 34400/6
∴ Selling price per kg for the remaining tea = 41300/6 ÷ 50/6 = 688
A person spent Rs. 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is
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Answer:20000
Explanation :
Let the price of desktop be Rs. d, and laptop be Rs. (50,000 - d)
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
A.
50
B.
54
C.
60
D.
55
Answer: Option
A
Explanation :
Let the cost price be c and marked price be m. Total selling price for 12 toys = Rs. 12c.
Anil sells 8 toys at 20% discount. Hence, total selling price for 8 toys = 8 × 0.8m = 6.4m
He then sells 4 toys at further 25% discount. Hence, total selling price for 8 toys = 4 × 0.75 × 0.8m = 2.4m
Given, 6.4m + 2.4m = 2112
⇒ m = 240
Now, he earns an overall profit of 10%
∴ 12c × 1.1 = 2112
⇒ c = 160
∴ With no discounts his profit % = (240 - 160)/160 × 100 = 50%
A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to
A.
25
B.
35
C.
22
D.
31
Answer: Option
A
Explanation :
Let the cost price of sugar be Rs. 100/kg and marked price will be = Rs. 120/kg
∴ Total cost for the man = 35 × 100 = Rs. 3500
He earns 15% profit on this, hence total selling price = 3500 × 1.15 = Rs. 4025
Total Selling price for 5 kg sugar = 5 × 120 = 600
Total Selling price for 15 kg sugar = 15 × 120 × 0.9 = 1620
Total Selling price for 3 kg sugar = 3 × 0 = 0
Total Selling price for remaining 12 kg sugar = 12 × 120(1 + p%)
Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was
A.
2000
B.
6000
C.
8000
D.
4000
Answer: Option
D
Explanation :
Let the cost price of one bicycle = Rs. x
Total cost price = Rs. 10x
He made a total profit of 25% on 6 cycles and 25% loss on 4 cycles and made a profit of Rs. 2000
A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x - y) / p equals
A.
1
B.
1.2
C.
0.7
D.
0.5
Answer: Option
A
Explanation :
The Shopkeeper procures the table at price 'p'
He gains 20% on the transaction with Amal
So, Amal buys the table at '1.2p'
Amal sells athe table at 30% profit,
So, the Selling Price of Amal = 1.3 × 1.2p = 1.56p
⇒ x = 1.56p
The Shopkeeper loses 20% on the transaction with Asim
So, Asim buys the table at '0.8p'
Asim sells the table at 30% loss,
So, the Selling Price of Asim = 0.7 * 0.8p = 0.56p
A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?
A.
86
B.
84
C.
98
D.
96
Answer: Option
D
Explanation :
Assume that the wholesaler bought peanut at Rs. X per kg.
∴ Cost price of walnuts = Rs. 3X per kg
The wholesaler sold peanuts at Rs. 1.1X per kg and walnuts at Rs. 3.6X per kg.
Total cost of 8 kg peanuts and 16 kg walnuts for the shopkeeper
= 8 × 1.1X + 16 × 3.6X = 66.4X
Shopkeeper overall profit was 25%
Therefore, revenue = 66.4X × 1.25
He sold (8 – 3 =) 5 kg peanuts and (16 – 5 =) 11 kg walnuts after mixing at Rs. 166 per kg
Therefore, 66.4X × 1.25 = 16 × 166
Solving this, we get
X = 32
Cost price of walnuts for the wholesaler = 3 × 32 = Rs. 96
Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
A.
17 : 25
B.
18 : 25
C.
21 : 25
D.
19 : 24
Answer: Option
D
Explanation :
Let cost of tea A and B be a and b respectively.
If 3 kg of tea A is mixed with 2 kg of tea B, (3a + 2b) × 1.1 = 40× 5 = 200
If 2 kg of tea A is mixed with 3 kg of tea B, (2a + 3b) × 1.05 = 40× 5 = 200
A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is
A.
20
B.
26
C.
16
D.
22
Answer: Option
A
Explanation :
Let the 10 litres of mixture has ‘Y’ litres of A and (10 – Y) litres of B. Let cost of paint B be Rs. X and that of A be Rs. (X + 8).
We know that, Y ≥ (10 – Y) ⇒ Y ≥ 5
The trader makes 10% profit by selling this mixture at Rs. 264.
∴ Cost price of the mixture = = Rs. 240
∴ (X + 8) × Y + (10 – Y) × X = 240
∴ 10X + 8Y = 240
∴ X = 24 – 0.8Y
For maximum value of X, we need to consider minimum value of Y.
In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is:
If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?
A.
30%
B.
25%
C.
24%
D.
28%
Answer: Option
D
Explanation :
Let the printed price be p.
If 40% discount is given, selling price = 0.6 × 60p = 36 p
20% profit is then made.
Total cost price = 36p/1.2 = 30p.
Ten toys are destroyed in the fire.
The remaining toys are sold at a price such that the same amount of profit is made as in the conditional case.
The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is
A.
1500
B.
2000
C.
2500
D.
3000
Answer: Option
B
Explanation :
Lets the manufacturers C.P. be 100
As he sells it to the wholesaler at 10% profit, his S.P will be 100 + 10 or 110
Now 110 is also the wholesaler’s C.P. Further, as the wholesaler sells it to a retailer at 30%, profit, his S.P will be
× 100 = 143.
Now 143 also the retailers C.P
As the retailer sells it to the customer at
50% profit, S.P. will be × 143 or 214.5
Now 214.5 is the price the customer pays for the table, when the manufacturer’s cost is 100.
Let the manufacturer’s cost of the table be Rs. ‘x’ when the price paid by the customer is Rs. 4290
Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?
A.
50
B.
30
C.
25
D.
45
Answer: Option
A
Explanation :
Supposing Mayank buys ‘x’ dozen candies at Rs. 15 per dozen and another ‘x’ dozen candies at Rs. 12 per dozen.
Total C.P =15(x) + 12(x) per dozen.
Now he sells these ‘x + x’ or ‘2x’ dozen candies at Rs. 16.50 per dozen.
So total S.P = 16.50 × 2x = 33x
Profit = 33x -27x = 6x
Now 6x = 150 or x = 25
As Mayank buys ‘2x’ dozen candies, number of dozens of candies bought by him
A leather factory produces two kinds of bags, standard and deluxe. The profit margin is Rs. 20 on a standard bag and Rs. 30 on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times per bag on the two machines are as follows:
The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit?
A.
Standard 75 bags, Deluxe 80 bags
B.
Standard 100 bags, Deluxe 60 bags
C.
Standard 50 bags, Deluxe 100 bags
D.
Standard 60 bags, Deluxe 90 bags
Answer: Option
A
Explanation :
Total time available is 700 hrs on machine A and 1250 hrs on machine B.
Let the number of Standard Bags be s and the number of Deluxe Bags be d.
Here we have to maximize the profit margin i.e. 20s + 30d, subject to the constraints,
4s + 5d ≤ 700 and 6s + 10d ≤ 1250
Now consider options.
1. s = 75 and d = 80
∴ The profit = 75 × 20 + 30 × 80 = 3900
4s + 5d = 700 and 6s + 10d = 1250
∴ the constraints are satisfied.
2. s = 100 and d = 60
∴ The profit = 100 × 20 + 60 × 30 = 3800
The profit is less than in option 1.
∴ Option 2 is not the answer.
3. s = 50 and d = 100
∴ The profit = 50 × 20 + 100 × 30 = 4000
4s + 5d = 700 and 6s + 10d = 1300
∴ The second constraint is not satisfied.
∴ Option 3 cannot be the answer.
4. s = 60 and d = 90
∴ The profit = 60 × 20 + 90 × 30 = 3900
4s + 5d = 690 and 6s + 10d = 1260
∴ The second constraint is not satisfied.
∴ Option 4 cannot be the answer.
As only option 1 satisfies the constraints and also maximizes the profit, option 1 is the answer.
Each question is followed by two statements A and B. Answer each question using the following instructions:
Answer (1) if the question can be solved by any one of the statements, but not the other one.
Answer (2) if the question can be solved by using either of the two statements. Answer (3) if the question can be solved by using both the statements together and not by any one of them. Answer (4) if the question cannot be solved with the help of the given data and more data is required.
A dress was initially listed at a price that would have fetched the store a profit of 20% on the wholesale cost. What was the wholesale cost of the dress?
A. After reducing the listed price by 10% the dress was sold for a net profit of 10 dollars.
B. The dress was sold for 50 dollars.
Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone. Choose 2; if the question can be answered by using either statement alone. Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone. Choose 4; if the question cannot be answered even by using both statements together.
Harshad bought shares of a company on a certain day, and sold them the next day. While buying and selling he had to pay to the broker one percent of the transaction value of the shares as brokerage. What was the profit earned by him per rupee spent on buying the shares?
The sales price per share was 1.05 times that of its purchase price.
The number of shares purchased was 100.
A.
1
B.
2
C.
3
D.
4
Answer: Option
A
Explanation :
From Statement A
The cost of buying the shares for Harshad is
CP + 0.01 CP = 1.01 CP
The cost of selling the shares for Harshad is
SP – 0.01 SP = 0.99 SP
∴ Profit = Cost of selling – Cost of buying
= 0.99 SP – 1.01 CP
∵ SP = 1.05 CP
Profit = (0.99 × 1.05 CP) – 1.01 CP
= 0.0295 CP
∴ Profit earned per rupee spent on buying the shares is Rs 0.0295.
From the number of shares given in the statement B, we cannot conclude anything.
Direction: Answer the questions based on the following information.
A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German mark increased by 30% and that of USA dollar increased by 22%. Due to market conditions, the selling price cannot be increased beyond 10%.
Let CP = 100
Current gain = 20
⇒ SP = 120
CP = Cost of A + Cost of B + other
= 30% + 50% + 20%
Since cost of German mark (A) increase by 30%
New cost of A = 30 + 30% of 30 = 39
Similarly
New cost of B = 50 + 22% of 50 = 61
New CP = 39 + 61 + 20 = 120
New SP = 120 + 10% of 120 = 132
Maximum profit =
If the USA dollar becomes cheap by 12% over its original cost and the cost of German mark increased by 20%, what will be the gain? (The selling price is not altered.)
A.
10%
B.
20%
C.
15%
D.
7.5%
Answer: Option
B
Explanation :
Let CP = 100
Current gain = 20
⇒ SP = 120
CP = Cost of A + Cost of B + other
= 30% + 50% + 20%
New cost of A = 30 + 20% of 30 = 36
New cost of B = 50 – 12% of 50 = 44
New CP = 36 = 44 + 20 = 100
Gain = 20%
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?
A.
28.56%
B.
35%
C.
22.22%
D.
None of these
Answer: Option
A
Explanation :
Hint: Students please note that the percentages that are given are the basic percentages derived from basic fractions. e.g. 11.11% = and 14.28 =
Hence, you should make use of the most of this kind of knowledge. So let the CP be Re 1. Since he makes a profit of his SP = .
His marked price should be above this. So if we subtract of MP from the MP, we will get the SP.
So
Hence, MP =
Therefore, percentage of mark-up on CP = (MP – CP)/CP
= 2 × 14.28 = 28.56%
Alternative method:
We can use the formula z = x – y – where
z = Gain percentage
x = Percentage above CP
y = Discount percentage
∴ 14.28% = x – 11.11% –
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?
A.
Rs. 80
B.
Rs. 100
C.
Rs. 95
D.
None of these
Answer: Option
D
Explanation :
Let he mix 3 kg, 4 kg and 5 kg of dry fruits at Rs. 100, Rs. 80 and at Rs. 60 per kilogram respectively. Hence, his effective cost of the dry fruits per kilogram should be the weighted average
In order to make a 50% profit, he will have to sell it at = Rs. 115 per kg.
Since none of the answer-choices confirms this, the answer is (d).
Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?
A.
20%
B.
25%
C.
40%
D.
15%
Answer: Option
A
Explanation :
Let the price per metre of cloth be Re 1. The shopkeeper buys 120 cm, but pays for only 100 cm. In other words, he buys 120 cm for Rs. 100. So his CP = = Re 0.833 per metre. Now he sells 80 cm, but charges for 100 cm. In other words, he sells 80 cm for Rs. 100. On this he offers a 20% discount on cash payment. So he charges Rs. 80 for 80 cm cloth. In other words, his SP = = Re 1 per metre. So his percentage profit in the overall transaction =
Direction: Answer the questions based on the following information.
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
A.
Rs. 90,000
B.
Rs. 75,000
C.
Rs. 45,000
D.
Rs. 60,000
Answer: Option
B
Explanation :
Total expense incurred in making 1,500 watches = (1500 x 150) + 30000 = Rs. 2,55,000.
Total revenue obtained by selling 1,200 of them during the season = (1200 × 250) = Rs. 3,00,000. The remaining
300 of them has to be sold by him during off season. The total revenue obtained by doing that = (300 × 100)
= Rs. 30,000. Hence, total revenue obtained
= (300000 + 30000) = Rs. 3,30,000. Hence, total profit
= (330000 – 255000) = Rs. 75,000.
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?
A.
500
B.
700
C.
800
D.
1,000
Answer: Option
B
Explanation :
From the previous solution, we can see that the total expense incurred by him in manufacturing 1,500 watches
= Rs.2,55,000. In order to break-even, he has to make a minimum revenue in order to recover his expenditure. He gets Rs. 250 per watch sold and Rs. 100 on every watch not sold. Let him sell x watches to break-even. So our equation will be 250x + 100(1500 – x) = 255000. Solving this, we get x = 700 watches
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