Profit and Loss
Cost Price (C.P.)
The price at which an article is purchased or manufactured is called its cost price.
Selling Price (S.P.)
The price at which an article is sold, is called its selling price.
Profit
If the selling price of an article is greater than its cost price, we say that there is a profit or gain.
Profit = Selling Price - Cost Price
When S.P.>C.P.
- Profit = S.P. - C.P.
- S.P.= C.P.+Profit
- C.P.=S.P.-Profit
- Profit % = Profit/C.P. * 100
- Profit = Profit % * C.P.
- When C.P. and Profit% are given then, S.P. = C.P. * ((100+Profit %)/100)
- When S.P. and Profit % are given then C.P.= 100* S.P./100+ Profit %
Loss
If the selling price of an article is less than tits cost price, we say that there is a loss.
Loss = Cost Price - Selling Price
- Loss = C.P. - S.P.
- S.P.= C.P.-Loss
- C.P.=S.P.+Loss
- Loss % = Loss/C.P. * 100
- Loss = Loss % * C.P.
- When C.P. and Loss % are given then, S.P. = C.P. * ((100-Loss %)/100)
- When S.P. and Loss % are given then C.P.= 100* S.P./100- Loss %
Discounts:
Discount is always calculated on the Market price(M.P.) of the article.
- Discount = M.P.-S.P.
- Discount % = (Discount/M.P.) * 100
- S.P.= M.P.-Discount
- M.P.= S.P.+Discount
- When M.P. and Discount % are given S.P.= (M.P. * (100-Discount%))/100
- When S.P. and Discount % are given, M.P.=(S.P.*100)/100-Discount %
- If Profit is made. C.P.=M.P.- Discount - Profit
- If Loss is made C.P.= M.P.- Discount + Loss
Successive Discounts
When a series of discounts are given we call them Successive Discounts.
Note: When an article is sold after two successive Discounts of P% and Q%, then the final Selling Price
S.P.= M.P.*(100-P%)(100-Q%)/100*100.
Suppose an item is sold after successive discounts of P% Q% & R%, Then its final selling price is given by
S.P.= M.P.* (100-P%)(100-Q%)(100-R%)/100*100*100
For example when two successive discounts of 10% and 20% are given, then the selling price is
S.P.= M.P.(100-10)(100-20)/100*100.
Let M.P. be 100, S.P.=100*90*80/100*100=7200/100=72
Effective Discount = M.P.-S.P.=100-72=28%
The combined value of Discounts = 10+20=30%. We observe that effective discount, 28% is less than 30%.
Note: The effective Discount obtained after successive discounts is always less than a discount whose percentage equals the sum of the successive discounts percentages offered on an article. In other words, the effective discount, due to successive discounts of P%, Q%, & R% is always less than (P+Q+R)%.
Question: Rahul sold his bicycle after offering 10% discount. If he had sold it after offering another discount of the same amount, his selling price would have been Rs.480. find his marked prices?
Solution: Let x be the marked price.
S.P.=M.P. - Discount
480=x-2(10/100)x
x=600
Question: Raja marked a toy at Rs.400. He sold it without offering a discount. If his cost price is Rs.300, find his profit percentage?
Solution: Selling Price S.P.=400
Cost Price C.P.=300
Profit %=?
Profit = S.P. - C.P.
=100
Profit %= (Profit/C.P.) * 100
= 100/300 *100
= 33.33%
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Question: Ashok purchased some goods for Rs.600. He sold one third of them at 20% profit. At what profit percentage should he sell the remaining to obtain an overall profit of 33 1/3%?
Solution: Let total selling price of Ashok be Rs.x
Total profit of Ashok =1/3* 600 = Rs.200
x=200+600=800.
Selling price of one-third of goods.
=600/8+20/100*(600/8)= Rs.240.
Selling price of the remaining goods= 800-240=Rs.560
Profit percentage at which the remaining goods must be sold= ((560-2/3(600))/2/3(600))*100=40%
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Question: Govind bought some apples at the rate of 25 for Rs.20 and an equal number at the rate of 30 for Rs.18. He then sold all at the rate of 20 for Rs.19. Find his profit/Loss percentage?
Solution: Let us say Govind bought x apples at each rate.
Total cost price of Govind= 20x/25+18x/30=Rs.1.4x
Total Selling price of Govind = 19/20(2x)=1.9x
As total selling price of Govind exceeds the total cost price of Govind, he makes a profit
His profit % = (profit/CP)*100=((SP-CP)/CP) *100= 1.9x-1.4x/1.4x*100=35 5/7%
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Question: Raja bought 15 kg of refined oil for Rs.450. He was forced to sell it at a loss equal to the selling price of 3 kg of refined oil. At what price did he sell it?
Solution: Let the selling price of each kg of refined oil is x
Loss of Raja = 3x
Loss = C.P. - S.P.
3x = 450-15x
18x=450
x=25
The selling price of Raja is Rs.25/kg.
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Question: Prasad bought two bags for a total of Rs.400. He sold one at 10% profit and another at 10% loss. If he bought each bag at the same price, find his total selling price?
Solution: When cost price of two articles are the same and one is sold at x% profit and the other is sold at x% loss, on the overall neither profit nor loss is made.
In this problem x=10.
The total selling price= total cost price.
=Rs.400.
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Question: Ashok started a business with an investment of Rs.10,000. After a few month, Alok joined him with an investment of Rs.12,000. At the end of one year from the start, they shared the total profit equally. After how long did Ashok join?
Solution: Ratio of profits of Ashok and Alok = Ratio of (investment time of Ashok and Alok).
Let us say Alok joined after x months.
10000(12):12000(12-x)
x=2
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Question: Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, Twice the investment of Bhavan and the investment of Chetan are equal. find the ratio of their respective profits at the end of one year?
Solution: Let the investments of Ajay, Bhavan and Chetan be Rs.a, Rs.b, and Rs.c respectively.
3a=2b=c
a=c/3 b=c/2
Ratio of profits of Ajay,Bhavan and Chetan at the end of one year = Ratio of their respective investments =2:3:6
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Question: Praveen and Naveen started a business with investments of Rs.20000 and Rs. 24000 respectively. At the end of one year, the total profit they shared was Rs.1000 more than the difference in their profit shares. find the total profit?
Solution: Ratio of profits of Praveen and Naveen =Ratio of their respective investments=5:6
Let the profit shares of Praveen and Naveen be 5x and 6x respectively.
6x+5x=6x-5x+1000
x=100
Total profit 11x=1100.
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Question: The selling price of 15 oranges is equal to the cost price of 12 oranges. find the profit / Loss percentage?
Solution: Let the C.P of each orange be Rs.1 C.P. of 15 oranges =Rs.15.
Selling price of 15 oranges =Cost price of 12 oranges =Rs.12
Loss is made in selling 15 oranges as their selling price is less than their cost price.
Loss made in selling 15 oranges = Rs.3
Loss%=20%.
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1. If the selling price of an article is obtained by multiplying the cost price by 4/5, then there is
a)20% profit b)20% Loss c)15% Profit d)15% Loss
Answer: Let Cost price C.P.=x
Given Selling price S.P.= C.P.* 4/5=4x/5.
S.P
Loss=C.P-S.P.
=x-4x/5
=5x-4x/5
=x/5
Loss % = Loss/C.P. * 100
= x/5/x*100
=1/5*100
=20%
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2.If the cost price of an article is obtained by multiplying the selling price by 8/9, then there is
a)25% profit b)25% Loss c)12.5% Profit d)12.5% Loss
Answer: Let Selling Price S.P. =x
Given Cost Price = x* 8/9=8x/9
S.P.>C.P.
Profit = S.P. - C.P.
=x-8x/9
=9x-8x/9
=x/9
Profit % = Profit/C.P. * 100
=x/9/8x/9 *100
=1/8*100
=12.5%
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3.If the selling price of an article is Rs.81, loss is 10%, then cost price is
a)Rs.90 b)Rs.71 c)Rs.72 d)Rs.91
Answer: Given S.P.=Rs.81
Loss % =10% C.P.=?
Let x be the C.P.
Loss = C.P.-S.P.
= x-81
Loss %= Loss/C.P. * 100
10=x-81/x * 100
10x=(x-81)*100
10x=100x-8100
90x=8100
x=90
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4.If a trader sold two cars each at Rs.325475 and gains 12% on the first and loses on 12% on the second, then his profit or loss percent on the whole is
a)1.44% Loss b)14.4% Profit c)14.4% Loss d)Neither profit nor loss
Answer: Let x1 be the Cost price of the first car.
and x2 be the cost price of the second car.
Given selling price of each cars are 325475. => S.P.1=325475, S.P.2=325475
Profit % of first car =12 %
Loss % of second car = 12%
Since if there are two articles having the same selling price one sold at x% profit and other sold at x% loss, Effectively a loss will always be made and the loss percent is
(x/10)^2.
Given x=12
(12/10)^2=144/100
1.44% loss.
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5.If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs.105 more. What is the cost price.
a)Rs.1505 b)Rs.1510 c)Rs.1500 d)Rs.1490
Answer: Let x be the cost price.
The difference of two profits percentage gives profit%
19-12=7% profit
Profit % = Profit/c.p. * 100
7=105/x*100
7x=105*100
7x=10500
x=1500
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6. A fruit vendor purchased 21 apples for Rs.180. Because of higher temperature, 33 1/3 % of apples are rotten and had to be thrown away. What price should the trader charge per apple if he wants to earn a profit of 16 2/3%?
a)Rs.22 b)Rs.25 c)Rs.16 d)Rs.15
Answer: Total 21 apples, 33.33% of apples are rotten.
21*1/3=7 apples were thrown away.
Remaining 14 apples are there.
Profit % =16.66%
Initial Selling price for 21 apples is Rs.180. In order get 16.66% profit .
180*1/6=30
Total Selling price =180+30=210
For 14 apples =210/14=15.
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7. Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did the Sreenivas purchase the table if Mahesh paid Rs.2178?
a)Rs.2100 b)Rs.2150 c)Rs.2200 d)Rs.2250
Answer: Selling price of Shiva to Mahesh is 2178
Loss % =10%
When S.P and Loss % is given then C.P.= 100* S.P./100-Loss %
C.P. = 100* 2178/100-10
=100* 2178/90
=2420
Here the cost price of Shiva becomes the selling price of Sreenivas.
Selling price of Sreenivas=2420
Profit %=10%.
When S.P. and Profit % is given then C.P. =100*S.P./100+Profit%
=100*2420/100+10
=10*2420/11
=2200.
So Sreenivas purchased the table at Rs.2200.
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8.A trader would incur a loss of 15%, if he sells pens at Rs.10.20 per pen. If 12.5% profit is to be earned after allowing 10% discount on the marked price then find the marked price?
a)Rs.13.5 b)Rs.15 c)Rs.17.2 d)Rs.12
Answer: Discount % =10%
Given loss% 15% and S.P.=10.20
C.P.=SP*100/100-loss%
=10.20*100/100-15
=1020/85
C.P. =12
Given profit % 12.5% and need to find marked price.
When C.P. and profit % are given then S.P.=CP* (100+Profit %) /100
=12*(100+12.5)/100
=12*112.5/100
S.P.=13.5
Let x be the M.P
When S.P. and Discount % are given, M.P.=(S.P.*100)/100-Discount %
x=(13.5*100)/100-10
=1350/90
=15.
The marked price is 15.
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9.A dishonest milk vendor purchased pure milk at Rs.10 per liter and sold diluted milk at Rs.10 per liter and gains a profit of 60%. What quantity of pure milk did he use in every liter?
a)625 ml b)600 ml c)400 ml d) 525 ml
Answer: Let the vendor purchased a 10 liters of milk at Rs.10 per liter.
Then the total amount of purchase is 100.
he gained 60% profit after diluting.
Let x be rate of milk per liter.
and y be the total amount of liters
and w be the water added in order to dilute.
%gain = (new amount-old amount)/old amount
0.6= (x(y+w)-xy)/xy
0.6=xy(1-1+w)/xy
w/y=0.6
w/y=6/10=3/5
This is clearly states that out of 8 liters, 3 liters of water is added with 5 liters of milk.
As per above statement total diluted milk =16 liters.
So there is 10 liters of pure milk in 16 liters of diluted milk.
Therefore each liter has a pure milk of =10/16 liters
=0.625 liters
=625 ml
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10.A trader loses 15% if an article is sold for Rs.102. find the selling price of the article to gain 20%.
a)Rs.150 b)Rs.144 c)Rs.138 d)Rs.132
Answer: Given loss % =15% and Selling price =102
C.P.=SP*100/100-Loss %
=102*100/100-15
=10200/85
=120
Given profit % is 20%, when C.P. and profit % is given.
S.P. = C.P*(100+profit%)/100
=120*(100+20)/100
=120*120/100
=144
The selling price is 144.
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11.A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent.
a)4% Loss b)4% Profit c)2% Loss d)2% Profit
Answer: Let cost price be 100
Then his marked price is 120.
If he allows discount of 20%. Find his loss or gain.
it means 80% of his marked price.
120*0.8=96
He is in loss 4%.
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12.The successive discounts 20% and 15% are equal to a single discount of
a)35% b)38% c)32% d)29%
Answer: The successive discount formula
S.P. = M.P.*(100-P)(100-Q)/100*100
Let M.P.=100
=100*(100-20)(100-15)/100*100
=100*80*85/100*100
=80*85/100
=68
S.P.=68
Effective discount = M.P.-S.P=100-68=32%
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13.If the cost price of 50 articles is equal to the selling price of 40 articles, the the gain or loss percent is
a)20% Loss b)20% Profit c)25% Profit d)25% Loss
Answer:
Given selling price of 40 articles=cost price of 50 articles.
Let the selling price of one article is Rs.1 each=selling price of 50 articles =Rs.50
cost price of 50 articles=selling price 40 articles=Rs.40
Profit made in selling article=10.
Profit %=25%
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14.A,B and C started a business with capitals of Rs.8000, Rs.10000 and Rs.12000 respectively. At the end of the year., the profit share of B is Rs.1500. The difference between the profit shares of A and C is.
a)Rs.300 b)Rs.400 c)Rs.500 d)Rs.600
Answer:
8000:10000:12000
8:10:12
4:5:6
Ratio of profits of A,B and C=Ratio of investments of A,B and C=4:5:6
let the profit shares of A,B and C are 4x,5x and 6x respectively.
4x+5x+6x=4x+1500+6x
5x=1500
x=300
Profit of A is 4x=1200
Profit of C is 6x=1800
The difference of the profit of A and C =1800-1200=600.
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15.A has started a business with an investment of Rs.70000 and after 6 months B joined him investing Rs.120000. If the profit at the end of a year is Rs.52000, then the share of B is
a)Rs.28000 b)Rs.24000 c)Rs.30000 d)Rs.27000
Answer: 70000(12):120000(12-6)
840000: 720000
7:6
Let the profits of A and B are 7x and 6x,
7x+6x=52000
13x=52000
x=4000
Then the share of B is 6x=6*4000=24000.
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16.Ram and Shyam started a business jointly, Ram's investment was thrice that of Shyam's and period of his investment was half that of shyam's. If Ram receives Rs.19200 as profit then their total profit is
a)Rs.28000 b)Rs.18800 c)Rs.32000 d)Rs.38000
Answer:Let x be the amount invested by Shyam.
Then the amount invested by Ram is =3x
Given Ram has joined half of the period of Shyam.
Ram(12-6):Shyam(12)
3x*6:x*12
18x:12x
3x:2x , 3:2
Given Ram receives a profit of 19200
Then the Total profit is
3x+2x=19200+2x
3x=19200
x=6400
Profit share of Ram=3x=19200
Profit share of Shyam=2x=12800
Total profit=19200+12800=32000.
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17.Ram, Robert and Raheem start a business. Ram invests one-third of the capital, Robert invests one-fourth of the capital and the rest is invested by Raheem. the share of Raheem in the total profit of Rs.240000 is
a)Rs.60000 b)Rs.80000 c)Rs.140000 d)Rs.100000
Answer:
Let x be the capital amount invested
Ram invested 1/3*x, Robert invested 1/4*x and Raheem invested 5/12*x
Ratio of investments
1/3x:1/4x:5/12x
1/3:1/4:5/12
Total profit of Ram,Robert and Raheem=Total investments of Ram,Robert and Raheem=1/3:1/4:5/12
Let the profit of Ram,Robert and Raheem is 1/3y,1/4y,5/12y
240000=1/3y+1/4y+5/12y
y=240000
The share of Raheem in total profit is 5/12*y=5/12*240000=100000.
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18.A,B and C invested total capital of Rs.60 lakhs in a business. B invested Rs.10 lakhs more than A and Rs.5 Lakhs more than C. What is the share of C out of a total profit of Rs.18 lakhs (Rs.in Lakhs)?
a)Rs.6 b)Rs.12 c)Rs.7.5 d)Rs.4.5
Answer:
From the above question it is clear that B invested 25 lakhs and A invested 15 lakhs and C invested 20 lakhs
Ratio of investments
15:25:20
3:5:4
Let the profit of shares of A,B and C are 3x,5x and 4x
The total profit of A,B and C=Total profit shares of A,B and C
18=3x+5x+4x
12x=18
2x=3
x=3/2
The profit share of C 4*x=4*3/2=6 lakhs.
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19. Bhuvan purchased a house site for Rs.120000 and house for Rs.320000.Then, he sold house site at 12% profit and house at 4.5% loss. Find his gain or loss percent in the total transaction.
a)4.5% b)7.5% c)3% d)None of these
Answer: Given house site C.P.=120000 and House C.P.=320000
he sold 12% profit house site and 4.5% loss house
When C.P. and Profit% are given then, S.P. = C.P. * ((100+Profit %)/100)
Then S.P.=120000*(100+12)/100
=1200*112
=134400
When C.P. and Loss% are given then, S.P.=C.P.*((100-loss%)/100)
Then S.P.=320000*(100-4.5)/100
=3200*(95.5)
=305600
Now sum of S.P=134400+305600=440,000
Sum of C.P.=120000+320000=440,000
It clearly states that there is no profit no loss. As S.p. and c.p. are equal in total transaction.
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20. Ratan purchased a gold coin and sold it to Keshav at 10% profit, As Keshav needs money, he sold it back to Ratan at the purchasing price of Ratan. Keshav incurred a loss of
a)9% b)11% c)9 1/11% d)11 1/9%
Answer:Let Ratan purchased the gold coin at Rs.100, then he sold it to Keshav at 10% profit.
Now C.P. of Keshav is 110. then again Keshav sold it back to Ratan at 100.
Keshav c.p.=110 and s.p.=100
Loss=110-100=10
Loss%=(loss/c.p.)*100
=10/110*100
=100/11
=9.090909
=9 1/11%.
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21.A fruit vendor purchased 20 dozens of bananas at Rs.15 per dozen. But one-fourth of bananas were rotten and had to be thrown away. He sold two-thirds of remaining bananas at Rs.22.50 per dozen. At what prize per dozen should he sell the remaining bananas to make neither profit nor loss.
a)Rs.20 b)Rs.15 c)Rs.22.50 d)Rs.7.50
Answer: Given 240 bananas at 300 rupees.
1/4th of Bananas were rotten=60 bananas.
Remaining 180 bananas.
in that 2/3 of bananas were sold at Rs.22.50 per dozen= 120 bananas @ Rs.225
remaining bananas are 60. Then he sold @ Rs.15 per dozen =Rs.75.
Answer is Rs.15 per dozen.
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22.A trader listed up the price of a product by 75%. If the discount is decreased from 50% to 25% then his profit raised by Rs.210. What is the cost of his product?
a)Rs.210 b)Rs.280 c)Rs.320 d)Rs.480
Answer: Let x be the cost price . Then the list price is 1.75x.
Discount is 25%. profit is 210
(1.75x/2-x)-(1.75x/4-x)=210
1.75x/4=210
1.75x=840
x=480
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23.A trader listed his products 25% above the cost price. He sells each product by allowing 10% discount for credit and by allowing two successive discounts of 10% each for cash payment. If he gets Rs.25 profit on each product on cash sales, then selling price of each product on credit sales is
a)Rs.2000 b)Rs.2225 c)Rs.2250 d)Rs.2500
Answer: Let the cost price be x. Then the Marked price is 1.25x.
If he allows 10% discount. Then Selling price=(marked price-0.10*marked price)
Selling price=(1.25x-0.10*1.25x)=1.125x for credit payment.
For cash sales
S.P.=M.P.(100-P)*(100-Q)/100*100
=1.25x(100-10)*(100-10)/100*100
=1.25x*90*90/100*100
=1.25x*81/100
=1.0125x for cash payment.
profit=25.
profit=S.P.-C.P.=1.0125x-x=0.0125x
25=0.0125x
x=2000
Now need to find the selling price on credit sales=1.125x=1.125*2000=2250
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24.A trader, by mistake, calculates his profit on the selling price and expresses it as 20%. What is the correct figure of his profit?
a)22% b)25% c)22 1/4% d)23 1/2%
Answer: We know that profit =S.P-C.P.
Let 100 be the cost price and selling price is 120. Given he has calculated 20% on selling price=120*.20=24.
C.P.=S.P-Profit=120-24=96
profit %= (profit/c.p.)*100
=(24/96)*100
=(3/12)*100=1/4*100=25%.
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25.After allowing a discount of 15% on marked price, the selling price is Rs.6800 for an article. He had sold it at marked price, he would have made a profit of 60%. cost price of the article is
a)Rs.6400 b)Rs.5600 c)Rs.5000 d)Rs.4800
Answer: Given selling price of an article =6800. Let x be the marked price.
We know that S.P.=(Marked price-0.15*Marked Price)=(x-0.15x)=0.85x
0.85x=6800
x=6800/0.85=8000
When S.P. and Profit % is given, then
C.P.= S.P*100/(100+Profit%) ,since profit% is attained by selling the product at M.P.
=8000*100/(100+60)
=8000*100/160
=8000*5/8
=5000
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26.By selling an item at 7/10th of the actual selling price, a trader makes a profit of 20%. If he sells the product at 20% less than the actual selling price, then what will be the profit or loss percentage?
a)30% b)20% c)37 1/7% d)33 1/3%
Answer:
27.The ratio of investments of A,B and C is 5:6:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments
a)2:3:4 b)3:5:6 c)3:2:4 d)2:4:3
28.X and Y started a business with capitals Rs.20000 and Rs.25000. After few months Z joined them with a capital of Rs.30000. If the share of Z in the annual profit of Rs.50000 is 14000, then after how many from the beginning did Z join?
a)7 months b)6 months c)5 months d)4 months.
29.P and Q started a business with respective investments of Rs.4 lakhs and Rs.10 lakhs . As P runs the business, his salary is Rs.5000 per month. If they earned Rs.2 lakhs of profit at the end of the year. then find the ratio of their earnings
a)2:5 b)5:2 c)3:5 d)1:1
30.A trader purchased an article with 20% discount, on the marked price from a distributor. What percent of discount on the marked price should the trader allow to gain 20%?
a)0% b)4% c)6% d)8%
31.A person gets Rs.3000 if he sells either article A at 10% profit and article B at 20% loss or article A at 10% loss and article B at 20% profit. The cost of A is?
a)Rs.1000 b)Rs.2000 c)Rs.1500 d)Rs.1250
32.A sold an article to B at 10% profit and B sold it to C at 15% profit. If B purchased for Rs.220, then find the difference in the purchasing prices of A and C
a)Rs.2000 b)Rs.2225 c)Rs.2250 d)Rs.2500
33.An article was sold at a profit of 20%. if both the cost price and selling price are decreased by Rs.3000, then the profit would be 25%. find the original cost price.
a)Rs.15000 b)Rs.30000 c)Rs.45000 d)Rs.60000
34.An article is sold at 10% profit. If its cost price is increased by Rs.20 and the selling price is increased by Rs.10, then the profit would be 1 1/9%. find the original cost price?
a)Rs.120 b)Rs.150 c)Rs.115 d)Rs.102
Answer:
35.By selling 99 pens, a trader gains the cost of 33 pens . Find the gain percentage.
a)33 1/3% b)50% c)25% d)66 2/3%
Answer:
Let Rs.1 be cost of each pen. The cost of 33 pens =33
if he sells 99 pens gains Rs.33 extra. it means 99+33=132
C.P.=99 AND SP=132
PROFIT=S.P-C.P
=132-99
=33
Profit %= profit/cp *100
=33/99*100
=33 1/3 %
When a series of discounts are given we call them Successive Discounts.
Note: When an article is sold after two successive Discounts of P% and Q%, then the final Selling Price
S.P.= M.P.*(100-P%)(100-Q%)/100*100.
Suppose an item is sold after successive discounts of P% Q% & R%, Then its final selling price is given by
S.P.= M.P.* (100-P%)(100-Q%)(100-R%)/100*100*100
For example when two successive discounts of 10% and 20% are given, then the selling price is
S.P.= M.P.(100-10)(100-20)/100*100.
Let M.P. be 100, S.P.=100*90*80/100*100=7200/100=72
Effective Discount = M.P.-S.P.=100-72=28%
The combined value of Discounts = 10+20=30%. We observe that effective discount, 28% is less than 30%.
Note: The effective Discount obtained after successive discounts is always less than a discount whose percentage equals the sum of the successive discounts percentages offered on an article. In other words, the effective discount, due to successive discounts of P%, Q%, & R% is always less than (P+Q+R)%.
Question: Rahul sold his bicycle after offering 10% discount. If he had sold it after offering another discount of the same amount, his selling price would have been Rs.480. find his marked prices?
Solution: Let x be the marked price.
S.P.=M.P. - Discount
480=x-2(10/100)x
x=600
Question: Raja marked a toy at Rs.400. He sold it without offering a discount. If his cost price is Rs.300, find his profit percentage?
Solution: Selling Price S.P.=400
Cost Price C.P.=300
Profit %=?
Profit = S.P. - C.P.
=100
Profit %= (Profit/C.P.) * 100
= 100/300 *100
= 33.33%
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Question: Ashok purchased some goods for Rs.600. He sold one third of them at 20% profit. At what profit percentage should he sell the remaining to obtain an overall profit of 33 1/3%?
Solution: Let total selling price of Ashok be Rs.x
Total profit of Ashok =1/3* 600 = Rs.200
x=200+600=800.
Selling price of one-third of goods.
=600/8+20/100*(600/8)= Rs.240.
Selling price of the remaining goods= 800-240=Rs.560
Profit percentage at which the remaining goods must be sold= ((560-2/3(600))/2/3(600))*100=40%
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Question: Govind bought some apples at the rate of 25 for Rs.20 and an equal number at the rate of 30 for Rs.18. He then sold all at the rate of 20 for Rs.19. Find his profit/Loss percentage?
Solution: Let us say Govind bought x apples at each rate.
Total cost price of Govind= 20x/25+18x/30=Rs.1.4x
Total Selling price of Govind = 19/20(2x)=1.9x
As total selling price of Govind exceeds the total cost price of Govind, he makes a profit
His profit % = (profit/CP)*100=((SP-CP)/CP) *100= 1.9x-1.4x/1.4x*100=35 5/7%
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Question: Raja bought 15 kg of refined oil for Rs.450. He was forced to sell it at a loss equal to the selling price of 3 kg of refined oil. At what price did he sell it?
Solution: Let the selling price of each kg of refined oil is x
Loss of Raja = 3x
Loss = C.P. - S.P.
3x = 450-15x
18x=450
x=25
The selling price of Raja is Rs.25/kg.
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Question: Prasad bought two bags for a total of Rs.400. He sold one at 10% profit and another at 10% loss. If he bought each bag at the same price, find his total selling price?
Solution: When cost price of two articles are the same and one is sold at x% profit and the other is sold at x% loss, on the overall neither profit nor loss is made.
In this problem x=10.
The total selling price= total cost price.
=Rs.400.
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Question: Ashok started a business with an investment of Rs.10,000. After a few month, Alok joined him with an investment of Rs.12,000. At the end of one year from the start, they shared the total profit equally. After how long did Ashok join?
Solution: Ratio of profits of Ashok and Alok = Ratio of (investment time of Ashok and Alok).
Let us say Alok joined after x months.
10000(12):12000(12-x)
x=2
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Question: Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, Twice the investment of Bhavan and the investment of Chetan are equal. find the ratio of their respective profits at the end of one year?
Solution: Let the investments of Ajay, Bhavan and Chetan be Rs.a, Rs.b, and Rs.c respectively.
3a=2b=c
a=c/3 b=c/2
Ratio of profits of Ajay,Bhavan and Chetan at the end of one year = Ratio of their respective investments =2:3:6
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Question: Praveen and Naveen started a business with investments of Rs.20000 and Rs. 24000 respectively. At the end of one year, the total profit they shared was Rs.1000 more than the difference in their profit shares. find the total profit?
Solution: Ratio of profits of Praveen and Naveen =Ratio of their respective investments=5:6
Let the profit shares of Praveen and Naveen be 5x and 6x respectively.
6x+5x=6x-5x+1000
x=100
Total profit 11x=1100.
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Question: The selling price of 15 oranges is equal to the cost price of 12 oranges. find the profit / Loss percentage?
Solution: Let the C.P of each orange be Rs.1 C.P. of 15 oranges =Rs.15.
Selling price of 15 oranges =Cost price of 12 oranges =Rs.12
Loss is made in selling 15 oranges as their selling price is less than their cost price.
Loss made in selling 15 oranges = Rs.3
Loss%=20%.
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1. If the selling price of an article is obtained by multiplying the cost price by 4/5, then there is
a)20% profit b)20% Loss c)15% Profit d)15% Loss
Answer: Let Cost price C.P.=x
Given Selling price S.P.= C.P.* 4/5=4x/5.
S.P
Loss=C.P-S.P.
=x-4x/5
=5x-4x/5
=x/5
Loss % = Loss/C.P. * 100
= x/5/x*100
=1/5*100
=20%
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2.If the cost price of an article is obtained by multiplying the selling price by 8/9, then there is
a)25% profit b)25% Loss c)12.5% Profit d)12.5% Loss
Answer: Let Selling Price S.P. =x
Given Cost Price = x* 8/9=8x/9
S.P.>C.P.
Profit = S.P. - C.P.
=x-8x/9
=9x-8x/9
=x/9
Profit % = Profit/C.P. * 100
=x/9/8x/9 *100
=1/8*100
=12.5%
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3.If the selling price of an article is Rs.81, loss is 10%, then cost price is
a)Rs.90 b)Rs.71 c)Rs.72 d)Rs.91
Answer: Given S.P.=Rs.81
Loss % =10% C.P.=?
Let x be the C.P.
Loss = C.P.-S.P.
= x-81
Loss %= Loss/C.P. * 100
10=x-81/x * 100
10x=(x-81)*100
10x=100x-8100
90x=8100
x=90
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4.If a trader sold two cars each at Rs.325475 and gains 12% on the first and loses on 12% on the second, then his profit or loss percent on the whole is
a)1.44% Loss b)14.4% Profit c)14.4% Loss d)Neither profit nor loss
Answer: Let x1 be the Cost price of the first car.
and x2 be the cost price of the second car.
Given selling price of each cars are 325475. => S.P.1=325475, S.P.2=325475
Profit % of first car =12 %
Loss % of second car = 12%
Since if there are two articles having the same selling price one sold at x% profit and other sold at x% loss, Effectively a loss will always be made and the loss percent is
(x/10)^2.
Given x=12
(12/10)^2=144/100
1.44% loss.
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5.If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs.105 more. What is the cost price.
a)Rs.1505 b)Rs.1510 c)Rs.1500 d)Rs.1490
Answer: Let x be the cost price.
The difference of two profits percentage gives profit%
19-12=7% profit
Profit % = Profit/c.p. * 100
7=105/x*100
7x=105*100
7x=10500
x=1500
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6. A fruit vendor purchased 21 apples for Rs.180. Because of higher temperature, 33 1/3 % of apples are rotten and had to be thrown away. What price should the trader charge per apple if he wants to earn a profit of 16 2/3%?
a)Rs.22 b)Rs.25 c)Rs.16 d)Rs.15
Answer: Total 21 apples, 33.33% of apples are rotten.
21*1/3=7 apples were thrown away.
Remaining 14 apples are there.
Profit % =16.66%
Initial Selling price for 21 apples is Rs.180. In order get 16.66% profit .
180*1/6=30
Total Selling price =180+30=210
For 14 apples =210/14=15.
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7. Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did the Sreenivas purchase the table if Mahesh paid Rs.2178?
a)Rs.2100 b)Rs.2150 c)Rs.2200 d)Rs.2250
Answer: Selling price of Shiva to Mahesh is 2178
Loss % =10%
When S.P and Loss % is given then C.P.= 100* S.P./100-Loss %
C.P. = 100* 2178/100-10
=100* 2178/90
=2420
Here the cost price of Shiva becomes the selling price of Sreenivas.
Selling price of Sreenivas=2420
Profit %=10%.
When S.P. and Profit % is given then C.P. =100*S.P./100+Profit%
=100*2420/100+10
=10*2420/11
=2200.
So Sreenivas purchased the table at Rs.2200.
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8.A trader would incur a loss of 15%, if he sells pens at Rs.10.20 per pen. If 12.5% profit is to be earned after allowing 10% discount on the marked price then find the marked price?
a)Rs.13.5 b)Rs.15 c)Rs.17.2 d)Rs.12
Answer: Discount % =10%
Given loss% 15% and S.P.=10.20
C.P.=SP*100/100-loss%
=10.20*100/100-15
=1020/85
C.P. =12
Given profit % 12.5% and need to find marked price.
When C.P. and profit % are given then S.P.=CP* (100+Profit %) /100
=12*(100+12.5)/100
=12*112.5/100
S.P.=13.5
Let x be the M.P
When S.P. and Discount % are given, M.P.=(S.P.*100)/100-Discount %
x=(13.5*100)/100-10
=1350/90
=15.
The marked price is 15.
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9.A dishonest milk vendor purchased pure milk at Rs.10 per liter and sold diluted milk at Rs.10 per liter and gains a profit of 60%. What quantity of pure milk did he use in every liter?
a)625 ml b)600 ml c)400 ml d) 525 ml
Answer: Let the vendor purchased a 10 liters of milk at Rs.10 per liter.
Then the total amount of purchase is 100.
he gained 60% profit after diluting.
Let x be rate of milk per liter.
and y be the total amount of liters
and w be the water added in order to dilute.
%gain = (new amount-old amount)/old amount
0.6= (x(y+w)-xy)/xy
0.6=xy(1-1+w)/xy
w/y=0.6
w/y=6/10=3/5
This is clearly states that out of 8 liters, 3 liters of water is added with 5 liters of milk.
As per above statement total diluted milk =16 liters.
So there is 10 liters of pure milk in 16 liters of diluted milk.
Therefore each liter has a pure milk of =10/16 liters
=0.625 liters
=625 ml
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10.A trader loses 15% if an article is sold for Rs.102. find the selling price of the article to gain 20%.
a)Rs.150 b)Rs.144 c)Rs.138 d)Rs.132
Answer: Given loss % =15% and Selling price =102
C.P.=SP*100/100-Loss %
=102*100/100-15
=10200/85
=120
Given profit % is 20%, when C.P. and profit % is given.
S.P. = C.P*(100+profit%)/100
=120*(100+20)/100
=120*120/100
=144
The selling price is 144.
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11.A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent.
a)4% Loss b)4% Profit c)2% Loss d)2% Profit
Answer: Let cost price be 100
Then his marked price is 120.
If he allows discount of 20%. Find his loss or gain.
it means 80% of his marked price.
120*0.8=96
He is in loss 4%.
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12.The successive discounts 20% and 15% are equal to a single discount of
a)35% b)38% c)32% d)29%
Answer: The successive discount formula
S.P. = M.P.*(100-P)(100-Q)/100*100
Let M.P.=100
=100*(100-20)(100-15)/100*100
=100*80*85/100*100
=80*85/100
=68
S.P.=68
Effective discount = M.P.-S.P=100-68=32%
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13.If the cost price of 50 articles is equal to the selling price of 40 articles, the the gain or loss percent is
a)20% Loss b)20% Profit c)25% Profit d)25% Loss
Answer:
Given selling price of 40 articles=cost price of 50 articles.
Let the selling price of one article is Rs.1 each=selling price of 50 articles =Rs.50
cost price of 50 articles=selling price 40 articles=Rs.40
Profit made in selling article=10.
Profit %=25%
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14.A,B and C started a business with capitals of Rs.8000, Rs.10000 and Rs.12000 respectively. At the end of the year., the profit share of B is Rs.1500. The difference between the profit shares of A and C is.
a)Rs.300 b)Rs.400 c)Rs.500 d)Rs.600
Answer:
8000:10000:12000
8:10:12
4:5:6
Ratio of profits of A,B and C=Ratio of investments of A,B and C=4:5:6
let the profit shares of A,B and C are 4x,5x and 6x respectively.
4x+5x+6x=4x+1500+6x
5x=1500
x=300
Profit of A is 4x=1200
Profit of C is 6x=1800
The difference of the profit of A and C =1800-1200=600.
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15.A has started a business with an investment of Rs.70000 and after 6 months B joined him investing Rs.120000. If the profit at the end of a year is Rs.52000, then the share of B is
a)Rs.28000 b)Rs.24000 c)Rs.30000 d)Rs.27000
Answer: 70000(12):120000(12-6)
840000: 720000
7:6
Let the profits of A and B are 7x and 6x,
7x+6x=52000
13x=52000
x=4000
Then the share of B is 6x=6*4000=24000.
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16.Ram and Shyam started a business jointly, Ram's investment was thrice that of Shyam's and period of his investment was half that of shyam's. If Ram receives Rs.19200 as profit then their total profit is
a)Rs.28000 b)Rs.18800 c)Rs.32000 d)Rs.38000
Answer:Let x be the amount invested by Shyam.
Then the amount invested by Ram is =3x
Given Ram has joined half of the period of Shyam.
Ram(12-6):Shyam(12)
3x*6:x*12
18x:12x
3x:2x , 3:2
Given Ram receives a profit of 19200
Then the Total profit is
3x+2x=19200+2x
3x=19200
x=6400
Profit share of Ram=3x=19200
Profit share of Shyam=2x=12800
Total profit=19200+12800=32000.
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17.Ram, Robert and Raheem start a business. Ram invests one-third of the capital, Robert invests one-fourth of the capital and the rest is invested by Raheem. the share of Raheem in the total profit of Rs.240000 is
a)Rs.60000 b)Rs.80000 c)Rs.140000 d)Rs.100000
Answer:
Let x be the capital amount invested
Ram invested 1/3*x, Robert invested 1/4*x and Raheem invested 5/12*x
Ratio of investments
1/3x:1/4x:5/12x
1/3:1/4:5/12
Total profit of Ram,Robert and Raheem=Total investments of Ram,Robert and Raheem=1/3:1/4:5/12
Let the profit of Ram,Robert and Raheem is 1/3y,1/4y,5/12y
240000=1/3y+1/4y+5/12y
y=240000
The share of Raheem in total profit is 5/12*y=5/12*240000=100000.
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18.A,B and C invested total capital of Rs.60 lakhs in a business. B invested Rs.10 lakhs more than A and Rs.5 Lakhs more than C. What is the share of C out of a total profit of Rs.18 lakhs (Rs.in Lakhs)?
a)Rs.6 b)Rs.12 c)Rs.7.5 d)Rs.4.5
Answer:
From the above question it is clear that B invested 25 lakhs and A invested 15 lakhs and C invested 20 lakhs
Ratio of investments
15:25:20
3:5:4
Let the profit of shares of A,B and C are 3x,5x and 4x
The total profit of A,B and C=Total profit shares of A,B and C
18=3x+5x+4x
12x=18
2x=3
x=3/2
The profit share of C 4*x=4*3/2=6 lakhs.
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19. Bhuvan purchased a house site for Rs.120000 and house for Rs.320000.Then, he sold house site at 12% profit and house at 4.5% loss. Find his gain or loss percent in the total transaction.
a)4.5% b)7.5% c)3% d)None of these
Answer: Given house site C.P.=120000 and House C.P.=320000
he sold 12% profit house site and 4.5% loss house
When C.P. and Profit% are given then, S.P. = C.P. * ((100+Profit %)/100)
Then S.P.=120000*(100+12)/100
=1200*112
=134400
When C.P. and Loss% are given then, S.P.=C.P.*((100-loss%)/100)
Then S.P.=320000*(100-4.5)/100
=3200*(95.5)
=305600
Now sum of S.P=134400+305600=440,000
Sum of C.P.=120000+320000=440,000
It clearly states that there is no profit no loss. As S.p. and c.p. are equal in total transaction.
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20. Ratan purchased a gold coin and sold it to Keshav at 10% profit, As Keshav needs money, he sold it back to Ratan at the purchasing price of Ratan. Keshav incurred a loss of
a)9% b)11% c)9 1/11% d)11 1/9%
Answer:Let Ratan purchased the gold coin at Rs.100, then he sold it to Keshav at 10% profit.
Now C.P. of Keshav is 110. then again Keshav sold it back to Ratan at 100.
Keshav c.p.=110 and s.p.=100
Loss=110-100=10
Loss%=(loss/c.p.)*100
=10/110*100
=100/11
=9.090909
=9 1/11%.
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21.A fruit vendor purchased 20 dozens of bananas at Rs.15 per dozen. But one-fourth of bananas were rotten and had to be thrown away. He sold two-thirds of remaining bananas at Rs.22.50 per dozen. At what prize per dozen should he sell the remaining bananas to make neither profit nor loss.
a)Rs.20 b)Rs.15 c)Rs.22.50 d)Rs.7.50
Answer: Given 240 bananas at 300 rupees.
1/4th of Bananas were rotten=60 bananas.
Remaining 180 bananas.
in that 2/3 of bananas were sold at Rs.22.50 per dozen= 120 bananas @ Rs.225
remaining bananas are 60. Then he sold @ Rs.15 per dozen =Rs.75.
Answer is Rs.15 per dozen.
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22.A trader listed up the price of a product by 75%. If the discount is decreased from 50% to 25% then his profit raised by Rs.210. What is the cost of his product?
a)Rs.210 b)Rs.280 c)Rs.320 d)Rs.480
Answer: Let x be the cost price . Then the list price is 1.75x.
Discount is 25%. profit is 210
(1.75x/2-x)-(1.75x/4-x)=210
1.75x/4=210
1.75x=840
x=480
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23.A trader listed his products 25% above the cost price. He sells each product by allowing 10% discount for credit and by allowing two successive discounts of 10% each for cash payment. If he gets Rs.25 profit on each product on cash sales, then selling price of each product on credit sales is
a)Rs.2000 b)Rs.2225 c)Rs.2250 d)Rs.2500
Answer: Let the cost price be x. Then the Marked price is 1.25x.
If he allows 10% discount. Then Selling price=(marked price-0.10*marked price)
Selling price=(1.25x-0.10*1.25x)=1.125x for credit payment.
For cash sales
S.P.=M.P.(100-P)*(100-Q)/100*100
=1.25x(100-10)*(100-10)/100*100
=1.25x*90*90/100*100
=1.25x*81/100
=1.0125x for cash payment.
profit=25.
profit=S.P.-C.P.=1.0125x-x=0.0125x
25=0.0125x
x=2000
Now need to find the selling price on credit sales=1.125x=1.125*2000=2250
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24.A trader, by mistake, calculates his profit on the selling price and expresses it as 20%. What is the correct figure of his profit?
a)22% b)25% c)22 1/4% d)23 1/2%
Answer: We know that profit =S.P-C.P.
Let 100 be the cost price and selling price is 120. Given he has calculated 20% on selling price=120*.20=24.
C.P.=S.P-Profit=120-24=96
profit %= (profit/c.p.)*100
=(24/96)*100
=(3/12)*100=1/4*100=25%.
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25.After allowing a discount of 15% on marked price, the selling price is Rs.6800 for an article. He had sold it at marked price, he would have made a profit of 60%. cost price of the article is
a)Rs.6400 b)Rs.5600 c)Rs.5000 d)Rs.4800
Answer: Given selling price of an article =6800. Let x be the marked price.
We know that S.P.=(Marked price-0.15*Marked Price)=(x-0.15x)=0.85x
0.85x=6800
x=6800/0.85=8000
When S.P. and Profit % is given, then
C.P.= S.P*100/(100+Profit%) ,since profit% is attained by selling the product at M.P.
=8000*100/(100+60)
=8000*100/160
=8000*5/8
=5000
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26.By selling an item at 7/10th of the actual selling price, a trader makes a profit of 20%. If he sells the product at 20% less than the actual selling price, then what will be the profit or loss percentage?
a)30% b)20% c)37 1/7% d)33 1/3%
Answer:
27.The ratio of investments of A,B and C is 5:6:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments
a)2:3:4 b)3:5:6 c)3:2:4 d)2:4:3
28.X and Y started a business with capitals Rs.20000 and Rs.25000. After few months Z joined them with a capital of Rs.30000. If the share of Z in the annual profit of Rs.50000 is 14000, then after how many from the beginning did Z join?
a)7 months b)6 months c)5 months d)4 months.
29.P and Q started a business with respective investments of Rs.4 lakhs and Rs.10 lakhs . As P runs the business, his salary is Rs.5000 per month. If they earned Rs.2 lakhs of profit at the end of the year. then find the ratio of their earnings
a)2:5 b)5:2 c)3:5 d)1:1
30.A trader purchased an article with 20% discount, on the marked price from a distributor. What percent of discount on the marked price should the trader allow to gain 20%?
a)0% b)4% c)6% d)8%
31.A person gets Rs.3000 if he sells either article A at 10% profit and article B at 20% loss or article A at 10% loss and article B at 20% profit. The cost of A is?
a)Rs.1000 b)Rs.2000 c)Rs.1500 d)Rs.1250
32.A sold an article to B at 10% profit and B sold it to C at 15% profit. If B purchased for Rs.220, then find the difference in the purchasing prices of A and C
a)Rs.2000 b)Rs.2225 c)Rs.2250 d)Rs.2500
33.An article was sold at a profit of 20%. if both the cost price and selling price are decreased by Rs.3000, then the profit would be 25%. find the original cost price.
a)Rs.15000 b)Rs.30000 c)Rs.45000 d)Rs.60000
34.An article is sold at 10% profit. If its cost price is increased by Rs.20 and the selling price is increased by Rs.10, then the profit would be 1 1/9%. find the original cost price?
a)Rs.120 b)Rs.150 c)Rs.115 d)Rs.102
Answer:
35.By selling 99 pens, a trader gains the cost of 33 pens . Find the gain percentage.
a)33 1/3% b)50% c)25% d)66 2/3%
Answer:
Let Rs.1 be cost of each pen. The cost of 33 pens =33
if he sells 99 pens gains Rs.33 extra. it means 99+33=132
C.P.=99 AND SP=132
PROFIT=S.P-C.P
=132-99
=33
Profit %= profit/cp *100
=33/99*100
=33 1/3 %
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