Arithmetic - Profit & Loss - Previous Year CAT/MBA Questions
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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
Text 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%
Workspace:
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
Text 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% –
or 14.28 =
or 1428 - 1111 = 88.89x
or x = 28.56% (Approximately)
Workspace:
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
Text 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).
Workspace:
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
Text 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 =
Workspace:
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
Text 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.
Hence, option (b).
Workspace:
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
Text 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.
Hence, option (b).
[Note: Do not be confused by the statement "he is able to sell all the watches". This is to tell you that if required to bread even he would be able to sell all watches.]
Workspace:
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?
- (a)
(+)10
- (b)
(-)1
- (c)
(+)1
- (d)
(-)10
Answer: Option B
Text Explanation :
In this case, we need not use the data that SP = Rs. 300 each. This has to be used only to figure out that the SP of both the articles is the same. Also since the profit percentage on one is equal to the loss percentage on the other, viz. 10% effectively, it will be a loss given by 1%. Hence, the correct answer is (–)1.
Hence, option (b).
Workspace:
A stockist wants to make some profit by selling sugar. He contemplates about various methods . Which of the following would maximise his profit?
I. Sell sugar at 10% profit.
II. Use 900 g of weight instead of 1 kg.
III. Mix 10% impurities in sugar and selling sugar at cost price.
IV. Increase the price by 5% and reduce weights by 5%.
- (a)
I or II
- (b)
II
- (c)
II, III and IV
- (d)
Profits are same
Answer: Option B
Text Explanation :
Profit percentage in each case is
(i) 10%
(ii)
(iii)
(iv)
Workspace:
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?
- (a)
100%
- (b)
80%
- (c)
75%
- (d)
66 2/3%
Answer: Option A
Text Explanation :
16 articles sold at priced 12 articles, is equivalent to discount of 25%
Hence, shop keepers offer two discounts of 20% and 25% respectively and still makes a profit of 20%
If c is the cost price of an article and m is the marked price, then 1.2 × c = m ×
⇒ m = 2c.
This means that he had marked his goods 100% above his cost price.
Workspace:
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