Jasmine Grover Study Abroad Expert
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Profit and Loss has always been one of the most important parts of CAT. A lot of questions from this chapter are also used in other Management entrance exams, such as the SNAP, CMAT, MAT, ATMA, etc.
We'll start by looking at what Profit & Loss means for a single transaction. In these kinds of deals, certain ideas are important. What they are:
The cost price (CP) of a product for a person is the price at which they buy it.
The price at which a person sells a product is the Selling price of the product(SP).
If the Selling price of the product is more than the cost price then, there is a gain or profit in the transaction.
Profit or Gain = SP – CP , (SP > CP)
If the Selling price of the product is less than the Cost price then , there is a loss in the transaction.
Note: The Selling Price of the seller is the Cost Price of the buyer.
Loss = CP – SP , (SP < CP)
Percentage Profit/Loss
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Percentage profit or Loss is calculated with respect to Cost Price(CP)
Profit % = \(\frac{SP - CP}{CP}\) x 100 = \(\frac{Profit}{CP}\) x 100.
Loss % = \(\frac{CP - SP}{Cp}\) x 100 = \(\frac{Loss}{CP}\) x 100.
Alternatively,
SP= (1 + Profit%) CP
SP= (1 – Loss%) CP
CP=(1 – Profit%) SP
CP=(1 + Loss%) SP
Types of Cost
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In day-to-day business transaction a businessman/trader faces three types of costs:-
- Direct Costs or Variable Costs- Cost connected with direct selling of product or service. This cost varies with every unit of the product sold. Example:- Raw materials used for manufacturing of phone parts.
- Indirect Costs or Fixed Costs – Cost incurred irrespective of the item or service sold. Example:- Setting up of new plants for expansion.
Example: Infrastructure investment for road connectivity by the government such as Roads, Bridges etc. comes under fixed cost. With the increase in the number of vehicles in the road the variable cost associated for maintenance of the infrastructure increases.
Common Gain or Loss Concept
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When two items are sold for the same price, but one makes a profit and the other loses money, and the percentage of profit and loss are the same. There is always a loss in this situation.
Loss % = \((\frac{Common \ Gain \ or \ Loss \% }{10})^2\)
| Example: A man sells two wristwatches. He makes 9% on one and loses 9% on the other, but the price he gets for each is $350. (1) percentage profit or loss (2) net amount of profit or loss Ans: (1) There will always be loss. And the percentage loss is equal to (9/10)2 i.e., 0.81% loss. (2) Cost price for the product = (1 + Loss%) x SP = (1+ 0.81/100) x 350 = $352.83 Net loss after the transaction = CP - SP =. $352.83 - $350 = $2.52.83 |
The concept of Margin or contribution Per unit
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The difference between a product's selling price and its variable cost is called the margin or the product's contribution. This profit margin helps pay for the fixed costs of selling the product or service.
The concept of the Break-even Point
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The break-even point is defined as the volume of sale at which there is no profit or no loss.
In other words, the break-even point is the number of units sold at which the company's sales equal its costs. This point is also called the break-even point.
Since a portion of each unit sold goes towards covering fixed costs, a company starts making a profit as soon as it sells more than the number of units needed to break even. On the other hand, when the number of units sold is less than the break-even point, the company loses money.
Profit = (Actual sales- Break even Sales) x Contribution per unit.
Loss = (Break Even sales – Actual Sales) x Contribution per unit.
Profit calculation on the Basis of equating the Amount Spent and the Amount earned
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By putting the money made and spent on the same scale. In this case, the amount of goods left can be used to show how much money was made. This is because the person going through the transaction has gotten back all of the money he spent, but he still has some goods left over after the transaction. These things that are left over can then be seen as the profit or gain for the person in question.
So, the amount of goods left is equal to the profit when money is the same. Goods sold are also a measure of cost in this case.
Percentage Profit = \(\frac{Goods \ Left}{Goods \ Sold}\) x 100
Concept of Mark up
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While selling goods and services businessman increases the CP by some percentage called markup percentage and the corresponding price is called marked price and the amount with which the CP is increased is called Markup price.
CP + Markup = Marked price
CP + Markup% on CP = Marked Price(MP)
If a trader provides discount after marking up the price over and above CP then:-
MP(1 – Discount%) = Selling Price.
Re-writing in terms of Cost price(CP)
CP(1+ Markup%)(1- Discount %)= SP
| Examples: When a fruit vendor sells 10 mangoes, he or she makes back the cost of 15 mangoes. Find the percentage of the profit. Ans: As the selling price and cost price are equated based on units sold and bought. Percentage Profit = (Goods left/ Goods sold) x100 = (10/15)x100 = 66.66% |
Sample Questions
Ques: A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
- 24
- 18
- 27
- 32
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Ans: C
Assuming merchant bought n goods
Total Cost price incurred = 20 x n
Total Selling Price = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
As the profit is at least 40%. Selling price should be at least 40% more than Cost price
2 + 4 + 6 + 8 ….n terms ≥ 1.4 x 20 n
2 (1 + 2 + 3 + ….n terms) ≥ 28n
n(n + 1) ≥ 28n
n2 + n ≥ 28n
n2 - 27n ≥ 0
n ≥ 27
Ques: Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
- 1440
- 1176
- 1680
- 2520
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Ans: C
Assume that the average purchase price of these almonds is x rupees per kilogramme.
When you combine 4 kilogrammes of cashews, 14 kilogrammes of peanuts, and six kilogrammes of almonds to obtain 24 kilogrammes of nuts, let's assume that each kilogramme of nuts costs x rupees per kilogramme.
Ankita intended to earn 1,752 by selling these 24 kilogrammes of almonds. Therefore, she anticipated a profit of 175224175224 = 73 from the sale of these 24 kilogrammes of almonds. Therefore, the price per kilogramme of these 24 kilogrammes of almonds is 'x plus 73'.
She earns a total profit of 744 by selling 4 kilogrammes of the mélange at the marked price and the remainder at a 20% discount off the marked price.
This indicates that 4(x + 73) + 0.80 * 20(x + 73) = 24 x + 744 716 = 4x x = 179.
Thus, the price of 24 kilogrammes of these almonds is 24x = 24(179) = 4296.
In other terms, the cost of 4 kilogrammes of cashews, 14 kilogrammes of peanuts, and 6 kilogrammes of almonds is 4296.
It is stated that the price of 7 kilogrammes of cashews is equivalent to 30 kilogrammes of peanuts or 9 kilogrammes of almonds.7C = 30 P = 9 A
Where C, P and A are the per kg buying costs of Cashews, Peanuts and Almonds respectively.
Let 7C = 30 P = 9 A = 630k
C = 90k
P = 21k
A = 70k
We know that, the buying price of 4 kg cashews, 14 kg peanuts and 6 kg almonds is ₹4296.
4 C + 14 P + 6 A = 4296
4 (90k) + 14 (21k) + 6 (70k) = 4296
360k + 294k + 420k = 1074k = 4296
k = 4
A = 70k = 280
The buying price of Cashews is ₹280 per kg.
The total money spent on Cashews is 6C = ₹1680
Ques: Traders A and B purchase two items for 1000 and 2000 rupees, respectively. Trader A increases the price of his products by x%, whereas trader B increases the price by 2x% and offers a discount of x%. Find x if both produce the same non-zero profit.
- 25%
- 5%
- 5%
- 40%
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Ans: A
SP of trader A = 1000 (1 + x).
Profit of trader A = 1000 (1 + x) – 1000.
MP of trader B = 2000 (1 + 2x).
SP of trader B = 2000 (1 + 2x) (1 – x).
Profit of trader B = 2000 (1 + 2x) (1 – x) – 2000.
Both make the same profit => 1000 (1 + x) – 1000 = 2000 (1 + 2x) (1 – x) – 2000
1000x = 2000 – 4000x2 + 4000x – 2000x – 2000
4000x2 -1000x = 0
1000x (4x – 1) = 0
=> x = 25%
Ques: Two stores, P and Q, that sell the same model of TV set put the same price on it. P gives discounts of 20% and then 15%, while Q gives discounts of 18% and then 17%. From whom would it be better to buy the TV set?
- From P
- From Q
- Indifferent between the two
- Cannot be determined
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Ans: A
Assume marked price for both to be 100.
P’s selling price = 100 x 0.8 x 0.85 = 68
Q’s selling price = 100 x 0.82 x 0.83 = 68.06. Buying from ‘P’ is more profitable.
Ques: 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?
- Rs. 300
- Rs.320
- Rs. 345
- Rs.350
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Ans: A
Checking option (a): A buys at 300, sells to B at 345 for a 15% profit, and then B sells it back to A at 414 for a 20% profit, gaining $69 in the process. So, A's first price was Rs.300.
Ques: A Dealer sold two TV Sets for Rs.9600 each, gaining 20% in one and losing 20% on the other set. Find his net gain or net loss
- Rs. 400 loss
- Rs. 800 loss
- Rs. 400 gain
- Rs. 800 gain
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Ans: B
Net loss = (20/10)2 = 4% of the cost price. So, the total money made, Rs.19,200, is 96% of the value. So, the loss would be '800 and the cost price would be Rs. 20,000.
Ques: A 20% decrease in the price of sugar allows a householder to purchase 6 kilograms more for Rs. 240. How much did sugar originally cost per kilogram ?
- Rs.10 per kg
- Rs.6 per kg
- Rs. 8 per kg
- Rs. 5 per kg
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Ans: A
Reduction in price of sugar is 20% which means increase in amount of sugar by 25% i.e., 6kgs.
It means original amount of sugar needed = 6 x 4 = 24kgs
Original price of sugar = 240/24 = Rs. 10 per kg.
Ques: 400 rupees are required to service a Maruti automobile at Maruti care Pvt. Ltd. The manager of the service centre informed me that for the second service within a year, a customer can receive a 10% discount, and for the third and fourth service within a year, he can receive a 10% discount on the amount previously paid. Additionally, if a consumer receives more than four services within a year, he is required to pay only 60% of the service fees for these services. A customer received five services from the same service station. What is the customer's total percentage discount?
- 19.42%
- 18.5%
- 17.6%
- 26%
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Ans: A
Amount paid in 1st service = Rs.100
Amount paid in 2nd service = Rs.90
Amount paid in 3rd service = Rs.81
Amount paid in 4th service = Rs. 72.9
Amount paid in 5th service = Rs.60
Total amount paid= Rs. 403.9
Discount = 500 – 403.9= 96.1
Discount % = 96.1/500= 19.42%
Ques: Pankaj and Sushil invested some amount of money in the ratio of 3 : 5 for the same period in a business. They decided that at the end of year 20% profit was to be given to AIDS Control Society of India as a donation. Out of the remaining, 75% was to be reinvested and the rest of the profit was to be divided as interest on their capitals. If the difference in their shares is Rs.1200. Find the total profit?
- Rs.18000
- Rs.24000
- Rs. 20000
- None of these
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Ans: B
Let the total profit be 100
Amount left after donation = 80
Amount left after reinvestment = 20
Now, 5x/8 – 3x/8 =1200
Where, x is the amount left after reinvestment
2x=1200 ⇒ x=4800 8
Total Profit = 4800 x 5 = 24000
Ques: Rotomac produces very fine quality of writing pens. Company knows that on an average 10% of the produced pens are always defective, so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at ` 10 each. It estimates the overall profit on all the manufactured pens to be 25%. What is the manufacturing cost of each pen?
- Rs. 6
- Rs.5.6
- Rs.7.2
- Rs.8
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Ans: C
You should know that the company can only ship 90% of the pens it makes. So, if the price of making a pen is K, then the total income (including a 25% profit) is (8000 * K) 1.25. The same amount of money can be made by selling 90%-made pens for Rs.10, which is equal to 7200 10. So, (8000 K)1.25 = 7200 10 K = Rs. 7.2 (90% of 8000 = 7200)
Ques: Teenagers shoe company sells the shoes whose prices i.e., cost prices and selling prices are the multiples of either 13, 14, 15, 16, 17, 18 or 19, starting from ` 399 to ` 699 (i.e., 399 ,<= CP/SP ‚<= 699). What can be the maximum profit of the company?
- Rs. 292
- Rs. 398
- Rs. 298
- Rs. 300
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Ans: C
The maximum possible profit
= maximum possible difference in SP and CP.
It means SP be maximum and CP be minimum
CPmin = Rs.399, 19 m = 399
Where m is an integer
Again SPmin= Rs. 697, which is very close to 699.
Here, 697 = 17k, k is a positive integer.
So, the maximum profit = 697 – 399 = Rs. 298
Ques: Rajesh makes 750 articles, and each one costs him 60 paise. He sets the price so that even if only 600 items are sold, he will make back 40% of what he put into the business. But 120 items went bad, so he was only able to sell 630 items at this price. Find his actual profit as a percentage of his total cost, assuming that the items he didn't sell don't matter.
- 42%
- 53%
- 47%
- 46%
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Ans: C
Total outlay (initial investment) = 750 x 0.6 = Rs. 450.
By selling 600, he should make a 40% profit on the outlay. This means that the selling price for 600 should be 1.4 x 450 -> Rs.630
Thus, selling price per article = 630/600 = 1.05. Since, he sells only 630 articles at this price, his total recovery = 1.05 x 630 =Rs. 661.5
Profit percent (actual) = (211.5/450) x 100 = 47%
Ques: A company's records show that it made sales of Rs.12,600. The main cost is 35% of sales, and the cost of doing business is 25% of gross profit. To figure out the gross profit, you take out the primary cost plus the cost of advertising, which is Rs. 1400, plus the salary of the director, which is Rs. 650 per year, plus 2% of the annual sales as miscellaneous costs. Find the percentage return on a Rs. 14,000 capital investment.
- 35%
- 31%
- 28%
- Cannot be determined
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Ans: B
The following calculations will show the respective costs:
Primary Cost: 35% of 12600 = Rs.4410
Miscellaneous costs = 2% of 12600 = Rs.252
Gross Profit=12600–4410–1400–650–252= Rs.5888
Trading cost = 0.25 x 5888 = Rs.1472
Hence, Net profit = Rs.4416.
Percentage profit = 4416/14000 = 31.54%
Ques: When a man sells a TV for Rs. 33,000, he makes a 10% profit. He sells a second TV at a 20% loss. If, in the end, he doesn't win or lose, figure out how much the second TV set would sell for.
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Ans: The profit of 10% amounts to Rs.3000. This should also be the actual loss on the second TV.
Thus, the actual loss = Rs.3000 (20% of C.P.) Hence, the CP of the second set = Rs.15000. SP of the second TV set = 15000 – 3000 = Rs. 12000.
Ques: A and B have identical profit margins when selling articles for Rs. 1800 each, but A calculates his profit based on the selling price while B calculates it accurately based on the cost price, which is 20%. What is the difference between their respective profits?
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Ans: Profit of A = 1800 x (20/100) = Rs. 360.
Cost price of B = 1800/1.2 = Rs. 1500
Profit of B = (1800-1500) = Rs. 300
Difference of profit of A and B = Rs.60
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