Basic Study Notes & Quiz ( Profit & Loss)

Profit & Loss

Profit and loss are the terms related to monetary transactions in trade and business. Whenever a purchased article is sold, then either profit is earned or loss is incurred.

Cost Price (CP) :This is the price at which an article is purchased or manufactured.

Selling Price (SP): This is the price at which an article is sold.

Profit (SP>CP) :When an article is sold at a price more than its cost price, then profit is earned.

Loss (CP>SP) :When an article is sold at a price lower than its cost price, then loss in incurred.

Note : Profit and loss always calculated on cost price.

Some Important Concept

1. If a person sells two similar articles, one at a gain of a% and another at a loss of a%, then the seller always incurrs a loss which is given by

Loss%=(a/10)^2 %

2. If a'th part of some items is sold at x% loss, then required gain per cent in selling rest of the items in order that there is neither gain nor loss in whole transaction, is (ax)/(1-a)%

Example 1: A medical store owner purchased medicines worth Rs. 6000 form a company. He sold 1/3 part of the medicine at 30% loss. On which gain he should sell his rest of the medicines, so that he has neither gain or loss?

Here a = 1/3 , x = 30 % 
Required gain % = (1/3*30)/(1-1/3) = 15 % 

3. If cost price of 'a' articles is equal to the selling price of 'b' articles, then profit percentage 
=(a-b)*100/b

4. If a dishonest trader professes to sell his items at CP but uses false weight, then 

Gain %=Error*100/(True Value-Error)

Gain%=(True weight-False weight)/(False weight) X100%

Example 2: A dishonest dealer professes to sell his goods at cost price but he uses a weight of 930 g for 1 kg weight. Find his gain per cent.
Gain % = 70*100/930

5.If a shopkeeper sells his goods at a% loss on cost price but uses b g instead of c g, then his profit or loss is [(100-a)(c/b)-100]% as sign positive or negative

Example 3:A dealer sells goods at 6% loss on cost price but uses  14 g instead of 16 g. What is his percentage profit or loss?

Here a = 6 % , b = 14 g and c = 16 g 

Required answer = [(100-6)(16/14)-100]% = 7(3/7) %

6. If a dealer sells his goods at a% profit on cost price and uses b% less weight, then his percentage profit  will be 

(b+a)/(100-b)X100%

Example 4: A dealer sells his goods at 20% loss on cost price but uses 40% less weight. What is his percentage profit  or loss?

Here a = 20 , b = 40
Required answer = (40 -20)*100/(100- 40) = 33(1/3) %

7. If 'a' part of an article is sold at x% profit/loss, 'b' part at y% profit/loss and c part at z%  profit/loss and finally there is a profit/lossof Rs.R, then Cost price of entire article
=RS.(R*100)/(ax+by+cz) 

Example 5: If 2/3 part of an article is sold at 30% profit, 1/4 part at 16% profit and remaining part at 12% profit and finally, there is a profit of Rs.75, then find the cost price of the article.

Here a = 2/3 , x = 30 % , b =1/4 , y = 16 % , z = 12 % and R = 75 Rs

Required CP of article = (75*100)/(2/3*30+1/4*16+1/12*12)  = 7500/25 = 300

1. Aadesh bought a combined total of 25 monitors and printers. He marked up the monitors by 20% on CP while each printer was marked up by Rs. 2000. He was able to sell 75% of the monitors and 2 printers and make a profit of Rs. 49,000. The remaining monitors and 3 printers could not be sold by him. Find his overall profit or loss if he gets no return on unsold items and it is known that a printer costs 50% of a monitor.

(a) Loss of Rs. 48,500

(b) Loss of Rs. 21,000

(c) Loss of Rs. 41,000

(d) Data Inadequate

(e) None of these

2. A rickshaw dealer buys 30 rickshaws for Rs.4725. Of these, 8 are four seaters and rest are two seaters. At what price must he sell the four seaters so that if he sells the two seaters at 3/4th of this price, he makes a profit of 40% on his outlay.

(a) Rs. 180

(b) Rs. 270

(c) Rs. 360

(d) Rs. 450

(e) None of these

3. Ritesh bought 25 washing machines and microwave ovens for Rs. 2,05,000. He sold 80% of the washing machines and 12 microwaves ovens for a profit of Rs 40,000. Each washing machine was marked up by 20% over cost and each microwave oven was sold at a profit of Rs. 2,000. The remaining washing machines and 3 microwave ovens could not be sold. What is Raghav’s overall profit/loss?

(a) Rs. 1000 profit

(b) Rs. 2500 loss

(c) Rs. 1000 loss

(d) Cannot be determined

(e) None of these.

4. A flat and a piece of land were bought by two friends Tarun and Varun respectively at prices of Rs. 2Lakh and Rs. 2.2 Lakh. The price of the flat rises by 20% every year and that of land by 10% every year. After two years, they decided to exchange their possessions. What is approx. percentage gain of the gainer?

(a) 7.56%

(b) 6.36%

(c) 4.39%

(d) 3.36%

(e) None of these

5. Sunil calculates his profit percentage on the selling price whereas Sujeet calculates his profit on the cost price. They find that the difference of their profits is Rs. 900. If the selling price of both of them are the same, and Sunil gets 50% profit and Sujeet gets 40% profit, then find their selling price.

(a) Rs 4200

(b) Rs 4500

(c) Rs 4000

(d) Rs 4800

(e) None of these

6. A reduction of 10% in the price of salt enables a person to buy 2 kg more for Rs.180. Find the reduced and the original price per kg of salt respectively.

(a) Rs 10, Rs 9

(b) Rs 9, Rs 10

(c) Rs 18, Rs 20

(d) Rs 20, Rs 18

(e) Rs 18, Rs 16.2

7. A person sold his watch for Rs. 24. If the percentage of his loss was equal to the cost price , then the watch would have cost him

(a) Rs. 40

(b) Rs. 60

(c) Rs. 50

(d) Rs. 80

(e) None of these

8. A man buys two horses for Rs. 1550. He sells one so as to lose 23% and other so as to gain 27%. On the whole transaction he neither gains nor loses. What does each horse costs?

(a) 807,743

(b) 817,733

(c) 827,723

(d) 837,713

(e) None of these

9. An orange vendor makes a profit of 20% by selling oranges at a certain price. If he charges Rs. 1.2 higher per orange he would gain 40%. Find the original price at which he sold an orange.

(a) Rs. 3

(b) Rs. 12

(c) Rs. 4.8

(d) Rs. 6.0

(e) None of these

10. After selling a watch, shyam found that he had made a loss of 10%. He also found that had he sold it for Rs.27 more, he would have made a profit of 5%. the actual initial loss was what percentage of the profit earned,had he sold the watch for a 5% profit?

(a) 23%

(b) 150%

(c) 200%

(d) 180%

(e) None of these.

Answers & Explanation;

1. a
2. b
3. c
4. e  (8.189 approx. )
5. a
6. b
7. e (Either Rs 40 or Rs 60)
8. d
9. e (Rs. 3.60)
10. c

Explanation:

1.Total Number of printers = 5 (2 sold , 3 unsold)
Monitors = 20.
Profit made on Printers sold = 2000*2 = 4000.
Monitors sold = 20*75% = 15
Profit made on Monitors sold = 49000-4000 = Rs.45000.
Profit made per monitor = 45000/15 = 3000.
20% of CP of Monitor = 3000
CP of Monitor = 15000.
CP of Printer = 7500
Total CP = 15000*20 + 7500*5 = 3,37,500
Total SP = 18000*15 + 9500*2 = 2,89,000
Loss = 48,500 

2. Total investement = Rs. 4725
Total SP = 1.4*4725 = 6615
Now, Let the price of 4 seater be x then price of two seater will be .75x.
8x + 22*0.75x = 6615
24.5x= 6615 or x = 270

3.  Total number of Microwave ovens = 15 (12 sold +3 unsold)
Hence, Washing machines = 10
He sold 12 ovens and 8 washing machines
Hence, In total he sold 80% of both
Thus, He sells 80% of both at a profit of Rs. 40,000.
Cost of 80% of the goods = 0.8*2,05,000 = 1,64,000
Hence, Total SP = 1,64,000+40,000 = 2,04,000
CP = 2,05,000
Loss = Rs.1000

4. After 2 years :-
Flat would be worth = 2Lakh* 1.2*1.2 = Rs. 288000
Land would be worth= 2.2Lakh*1.1*1.1 = Rs. 266200
Profit of the Gainer = Rs. 21800
Profit % of the gainer = 21800*100/266200= 8.189(approx)
Also if loss% woudd have been asked of the loser
loss% = 21800*100/288000 = 7.56 (approx. )

5. Let SP be Rs. 100
CP for Sunil = => (SP-CP)*100/SP = 50
CP for Sunil ==> (100-CP)*100/100 = 50 or CP = Rs. 50
(Divided by SP as Profit calculated on SP)
Profit for Sunil = 100-50 = Rs 50
Now, CP for Sujeet = (SP-CP)*100/CP = 40
(100-CP)*100= 40CP or CP for Sujeet= Rs. 1000/14
Profit for Sujeet = 100-100/14 = 400/14
Now, Difference in profit when SP is 100 = 50-400/14 = 300/14.
Now, Equating difference and SP, we have
300/14 : 100 : : 900 : SP
SP = 900*100*14/300 = Rs. 4200

6 . Let originally he buy X kg for Rs. 180
Now, he will buy X+2 kg for Rs. 180.
Reduction in original price =10%
(180/X)/kg*90/100 = [180/(X+2)]/kg
90(X+2) = 100X
X = 18
Therefore, Originally he bought 18kg.
Original Price = Rs. 10/kg
Reduced Price = Rs. 9/kg

7. SP = Rs. 24
Let CP be X hence, Loss% = X
(X-SP)*100/X = X or (X-24)*100/X = X
X^2-100X+2400 = 0
(X-60)(X-40) = 0
X= 60 or 40

8. Let CP of one be X and other be Y
X+Y = 1550….(i)
ATQ:-
0.77X + 1.27Y = 1550…(ii) (as no profit and no loss is there)
Solving both, we get
50Y = 35650 or Y = 713
Hence, X = 1550-713 = 837
Therefore, CP of each horse = 837,713

9. Let the CP be Rs. x/ orange
Profit = 20%
SP = Rs. 1.20x
Now, If case :-
SP =x+ Rs.1.2
Profit = 40%
Therefore, we can say
1.40x = x+1.2 or x = Rs. 3
Hence, Original SP = Rs 1.2x = Rs. 3.60/-

10. Profit= 5% (If case )
5% of CP ------> Rs. 27
So, CP = Rs. 540
Now, Loss% = 10
Loss =Rs. 54
Required % = 54*100/27 = 200%

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