Home > Math Shortcuts > Profit and Loss Example Question & Answer

# Profit and Loss Example Question & Answer

## Profit and Loss Example Question & Answer

Example #1
A Seller 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 per cent above the cost price were his wares listed ?

MP=120/(80/100)=150
Now he is selling 16 goods to a dozen(ie, 12),
So, his loss = {(16-12)/16} x100 = 25%.
Then the actual MP 150/(75/100)=200.
Hence, he has marked the MP 100% above the CP.

Example #2
A Seller allowed a discount of 25% on marked price of Rs.20,000 on an article and incurred a loss of 20%. What discount should he allow on the marked price so that he gains Rs.450 on the article?

25% discount = 20,000 x 75 / 100 = 15000
Then loss 20% means
X x 80 / 100 = 15000 = 3750 x1054 24/855 = 18750
He gain 450 means SP = 18750 + 450 = 19200
Now 20000 – 19200 = 800
% = 800 / 20000 x 100 = 4%

Example #3
A Seller marked the price of an item 20% above cost price. He allowed two successive discounts of 20% and 25% to a
customer. As a result he incurred a loss of Rs.1400. At what price (in rupees) did he sell the item to the customer?

CP = 100
MP = 120
120 x 80 / 100 = 96; 96 x 75 / 100 = 72
Loss = 100 – 72 = 28%
CP = 100 / 28 x 1400 = 5000
SP = 5000 x 72 / 100 = 3600

Example #4
A shopkeeper bought a CD marked at Rs. 200 at successive discounts of 10% and 15% respectively. He spent Rs. 7 on
transport and sold the table for Rs.208 .What will be his profit percentage ?

Single equivalent discount for 10% and 15% = (15 + 10–(15×10/100))%= 23.5%
CP of CD = 200x(100-23.5)% = Rs.153
Expense on transport = Rs. 7
Actual CP = 153 + 7 = Rs. 160
Profit % = [(208–160)/160]x100 = 30%

Example #5
By selling 12 marbles for a rupee, a shopkeeper loses 20% . In order to gain 20% in the transaction , he should sell the marbles at the rate of how many marbles for a rupee?

SP of 12 marbles = Rs.1 , loss = 20%
CP of 12 marbles = Rs. (1/0.8) = Rs. 1.25
SP of 12 marbles at a gain of 20%
CP x 1.2 = 1.25 x 1.2

Example #6
A shopkeepar marked the price of an item 20% above cost price. He allowed two successive discounts of 20% and 25% to a customer. As a result he incurred a loss of Rs.1400. At what price (in rupees) did he sell the item to the customer?

CP = 100
MP = 120
120×80/100 = 96;
96×75/100 = 72
Loss = 100–72 = 28%
CP = 100/28×1400 = 5000
SP = 5000×72/100 = 3600

Example #7
A dishonest trader marks up his goods by 80% and gives discount of 25% . Besides he gets 20% more amount per kg from wholeseller and sells 10% less per kg to customer. What is the overall profit percentage ?

CP = 100/120 = 10/12
SP = 135/90 = 18/12
Profit % = {[(18/12) – (10/12)]/(10/12)} x100 = 80%.

Example #8
Titan sells a wrist watch to a wholeseller making a profit of 10%. The wholesaler sells it to the retailer making a profit of 10%. A customer purchases it by paying Rs.990. Thus the profit of retailer is 2(3/11)% what is the cost incurred by the Sonata to produce it?

[((X x 1.1)x1.1)x(1125/1100)] = 990
x = 800.

Example #9
A boy sold an electronic watch at Rs.96 in such a way that his percentage profit is same as the cost price of the watch . If he sells it at twice the percentage profit of its previous percentage then find the new selling price.

SP = X + (X x X)/100 = 96%
x = 60
New , SP = 60+(60×120)/100 = Rs.132.

Example #10
A trades man has 600kgs of rice ,a part of which he sells at 15% profit and the remaining quantity at 20% loss. On the whole , he incurs an overall loss of 6% .What is the quantity of rice he sold at 20% loss?

Quantity of rice sold at 20% loss = x kg (let)
Quantity of rice sold at 15% gain
= (600 – X ) kg (600 –X) x (115/100) + (X x 80)/100
= (600 x 94)/100
x = 12600/35
= 360 kg.

Example #11
A Seller sells Marker at the rate of Rs.35 each and earns a commission of 10%. He also sells Gel pen at the rate of
Rs. 65 each and earns a commission of 20%. How much amount (in rupees) of commission will he earn in 2 weeks, if he sells 12 markers and 8 Gel pens a day?

Commission for
marker=(35×12)x10/100=42
Commission for Gel pen
=(65×8)x20/100=104
Total Commission earned in 2 weeks is,
(104+42)x14=2044.

Example #12
A boy sells two fans for Rs. 6800. The cost price of the first fan is equal to the selling price of the second fan. If the first is sold at 30% loss and the second at 100% gain, what is total profit or loss (in rupees)?

Let the cp of 1st fan = sp of 2nd fan = Rs100
sp of 1st fan = 70(loss 30%)
Cp of 2nd fan = 50 (profit 100%)
Total cp = 100 + 50 = 150
and total sp = 70 + 100 = 170
When SP = 6800,
then cp = 150/170 x 6800 = 6000
Profit = 6800 – 6000 = 800.

Example #13
Titan sells a wrist watch to a wholeseller making a profit of 10%. The wholesaler sells it to the retailer making a profit of 10%. A customer purchases it by paying Rs.990. Thus the profit of retailer is 2(3/11)% what is the cost incurred by the Titan to produce it?

[((Xx1.1)X1.1)X(1125/1100)] = 990
X = 800.

Example #14
A and B are dealers of a bike company. The price of a bike is Rs.28,000. A gives a discount of 10% on whole , while B gives a discount of 12% on the first Rs.20,000 and 8% on the rest Rs.8000. What is the difference between their selling price?

A’ s discount = 2800
B’s discount = 2400+640 = 3040
Required difference = 3040-2800 = Rs.240.

Example #15
A bookseller procures 40 books for Rs.3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

CP = Rs. 3200/40 = Rs.80
Now SP of 40 books = CP of 40 books + SP of 8 books
SP of 32 books = 3200
SP of 1 book = Rs.100
Therefore, Required SP of 1 dozen books = Rs. 1200,

Example #16
If there is a loss of 40% when a good is sold at (2/5)th of its earlier selling price. Find the profit% after selling the good at a certain price.

CP = (2/3) of SP
SP = (100+P) / 100 of CP
Equating both the above equations,
Profit = 50%.

Example #17
By selling 144 hens Nilesh suffer a loss equal to the selling price of 6 hens. Find his loss percent?

loss = C.P – S.P
S.P of 6 hen = C.P of 144 hense – S.P of 144
hens
S.P of 150 hens = C.P of 144 hens
6/150 x100 = 4% loss.

Example #18
After selling 12 balls a boy suffer a loss equal to cost price of 6 balls. Find loss percent?

loss = CP-SP
CP of 6 ball = CP of 12 ball –SP of 12 ball
SP of 12 ball = CP of 6 ball
Loss % = 6/12×100= 50%.

Example #19
A boy wants to sell his goods at 20% profit after allowing a discount of 16 2/3% on marked price. How much % above the cost price should he mark his article?

Use formula:
MP = (100+p%)/(100-d%) x CP
OR
Profit%= 20% = 1/5 (profit = 1, CP = 5)
SP = CP+P = 5+1 = 6……(1)
Discount% = 16 2/3% = 50/3% = 1/6
(discount = 1, MP = 6)
Mp – discount = SP
6 – 1 = 5…………(2)
Make SP equal in both equations (1) and
(2)
Multiply (1) by 5 and (2) by 6
so CP : SP : MP = 25 : 30 : 36
So see CP and MP, required % = (36-25)/25 x 100 = 44%.

Example #20
By selling 20 Items, a person gains CP of 5 Items. Find the profit% incurred by him.

Profit = SP – CP
CP of 5 Items = SP of 20 Items – CP of 20 Items
So, CP of 25 Items = SP of 20 Items
Profit% = 5/20 x 100 = 25%.

Example #21
After selling a table worth Rs 12000 at 20% loss, a trader buys a TV with the same money. Next he sold the TV at 20% profit. What is his profit/loss in the whole transaction?
12000 – 2400 (20% loss) = 9600.
9600 + 1920 (20% profit on 9600) = 11520
So 12000 – 11520 = 480 Rs loss.

Example #22
A Company of a certain item can sell all items that he can produce at the selling price of Rs50 each. It cost him Rs30 in materials and labour to produce each item and he has overhead expenses of Rs5000 per week in order to operate the plant. The number of units he should produce and sell in order to make a profit of at least Rs3000 per week?

50x – (30x + 5000) = 3000
20x = 8000
x = 400.

Example #23
After selling 12 balls a man suffer a loss equal to cost price of 6 balls. Find loss percent?

loss = CP-SP
CP of 6 ball = CP of 12 ball – SP of 12 ball
SP of 12 ball = CP of 6 ball
Loss % = 6/12×100= 50%.

Example #24
A customer saves Rs400 at the rebate of 20% on market price of an article. If the cost price of the article for shopkeeper is Rs1200.Then find the profit percent of shopkeeper?

20% of M.P = 400
M.P = 2000
S.P = 1600
C.P= 1200
Profit % = 400/1200x 100= 33(1/3)%.

Example #25
After selling a table worth Rs 12000 at 20% loss, a trader buys a TV with the same money. Next he sold the TV at 20% profit. What is his profit/loss in the whole transaction?

12000 – 2400 (20% loss) = 9600
9600 + 1920 (20% profit on 9600) = 11520
So 12000 – 11520 = Rs.480  loss.

Example #26
A consumer sold his Items at cost price. But he used false weights and gives 800 gm instead of 1 kg. Find his profit%.

CP of 1000 gm = SP of 800 gm
So gain% = (1000-800)/800 x 100 = 25%.

Example #27
A shopkeeper sells Marker at the rate of Rs.35 each and earns a commission of 10%. He also sells Gel pen at the rate of Rs. 65 each and earns a commission of 20%. How much amount (in rupees) of commission will he earn in 2 weeks, if he sells 12 markers and 8 Gel pens a day?

Commission for
marker=(35×12)x10/100=42
Commission for Gel pen
=(65×8)x20/100=104
Total Commission earned in 2 weeks is,
(104+42)x14=2044.

Example #28
A dealer marked the price of an item 20% above cost price. He allowed two successive discounts of 20% and 25% to a
customer. As a result he incurred a loss of Rs.1400. At what price (in rupees) did he sell the item to the customer?

CP = 100
MP = 120
120×80/100 = 96; 96×75/100 = 72
Loss = 100 – 72 = 28%
CP = 100/28×1400 = 5000
SP = 5000×72/100 = 3600

Example #29
A dealer buys a product at Rs. 1920 , he sells at a discount of 20% still he gets the profit of 20% . What is the selling price of that product?

CP ——– SP ———-MP
100—-(20% profit)—-120——-(20%
discount) ——150
=> SP = 1.2CP = 2304

Example #30
A dishonest trader marks up his goods by 80% and gives discount of 25% . Besides he gets 20% more amount per kg from whole seller and sells 10% less per kg to customer. What is the overall profit percentage ?

CP = 100/120 = 10/12
SP = 135/90 = 18/12
Profit % = {[(18/12) – (10/12)]/(10/12)}x100 = 80%.

Example #31
A person sold an electronic watch at Rs. 96 in such a way that his percentage profit is same as the cost price of the watch . If he sells it at twice the percentage profit of its previous percentage then find the new selling price.

SP = X + (XxX)/100 = 96%
=> x = 60
New , SP = 60+(60×120)/100 = Rs. 132.

Example #32
Of the two varieties of rice available, variety A is bought at Rs.32 per kg and variety B at Rs.80 per kg. Two varieties of rice are mixed together in the respective ratio of 8:5 and the mixture is sold at Rs.72 per kg. What per cent of profit approximately the seller receives ?

Let 8 kg of first variety of rice and 5 kg of  second variety is mixed. CP of 13 kg of rice = (8×32 + 5×32) = Rs. 656
SP of 13 kg of rice = 72×13 = Rs.936 Profit = 936 – 656 = Rs.280 Profit% = (280/656)x100 = 43%.

Example #33
The percentage profit earned by selling an article for Rs. 2120 is equal to the percentage loss incurred by selling the
same article for Rs. 1520. At what price should the article be sold to make 25% profit?

The CP be
2120+1520=3640
3640/2=1820.
SP=1820×125/100=1820×5/4
=Rs2275

Example #34
A person X sold an Item to Y at 40% loss, then Y sold it to third person Z at 40% profit and finally Z sold it back to X at 40% profit. In this whole process what is the percentage loss or profit of X?

Let the CP = Rs.100. for X.
Y’s CP = Rs.60.
Z’s CP = Rs.84.
Finally, X’s CP = Rs.117.6.
:. X’s loss = 117.6 – 60 = Rs.57.6
:. X’s loss percent = 57.6%

Example #35
A shopkeeper sells Marker at the rate of Rs.35 each and earns a commission of 10%. He also sells Gel pen at the rate of Rs. 65 each and earns a commission of 20%. How much amount (in rupees) of commission will he earn in 2 weeks, if he sells 12 markers and 8 Gel pens a day?

Commission for
marker=(35×12)x10/100=42
Commission for Gel pen
=(65×8)x20/100=104
Total Commission earned in 2 weeks is,
(104+42)x14=2044.

Example #36
A dealer allowed a discount of 25% on marked price of Rs.20,000 on an article and incurred a loss of 20%. What discount should he allow on the marked price so that he gains Rs.450 on the article?

25% discount==>20,000×75/100=15000
Then loss 20% means
Xx80/100=15000=3750×5=18750
He gain 450 means SP=18750+450=19200
Now 20000-19200=800
%age =800/20000×100=4%

Example #37
A dealer marked the price of an item 20% above cost price. He allowed two successive discounts of 20% and 25% to a
customer. As a result he incurred a loss of Rs.1400. At what price (in rupees) did he sell the item to the customer?

CP = 100
MP = 120
120×80/100 = 96;

96×75/100 = 72
Loss = 100 – 72 = 28%
CP = 100/28×1400 = 5000
SP = 5000×72/100 = 3600.

Example #38
A dishonest trader marks up his goods by 80% and gives discount of 25% . Beside she gets 20% more amount per kg from whole seller and sells 10% less per kg to customer. What is the overall profit percentage ?

CP = 100/120 = 10/12
SP = 135/90 = 18/12
Profit % = {[(18/12) – (10/12)]/(10/12)}x100 = 80%.

Example #39
A bookseller procures 40 books for Rs.3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

CP = Rs. 3200/40 = Rs.80
Now SP of 40 books = CP of 40 books +
SP of 8 books
=> SP of 32 books = 3200
SP of 1 book = Rs.100
Therefore,
Required SP of 1 dozen books = Rs. 1200.

Example #40
An article is sold at 33(1/3)% profit. If it had been sold at a profit of 40%,it would have fetched Rs,50 more. Find cost price of article?

1st 33(1/3)% profit so CP = 3, and SP =
3+1 = 4
2nd 40% = 2/5. So CP = 5, SP = 7
Now CP is same so make CP same
CP…….. SP
15………..20
15………….21
20 to 21 is + 1, so 1= 50 [increase in SP]
So, 15=750.

Example #41
A calculate his profit %ge on the selling price whereas B calculate his on the cost price. They find that the difference of their profit is Rs 150. If the selling price of both of them are same and both of them get 20% profit, find their selling price (in rupees).

Let SP is x
A’s profit =x*20/120=x/6
B’s profit =x*20/100=x/5
Diff is x/6-x/5=150
x/30=150==>x=4500.

Example #42
A dealer allowed a discount of 25% on marked price of Rs.20,000 on an article and incurred a loss of 20%. What discount should he allow on the marked price so that he gains Rs.450 on the article?

25% discount==>20,000*75/100=15000
Then loss 20% means
x*80/100=15000=3750*5=18750
He gain 450 means SP=18750+450=19200
Now 20000-19200=800
%ge =800/20000*100=4%.

Example #43
If a shopkeeper sell a TV at 15% profit and a DVD at 12% loss then he earns Rs. 540 as total profit but if he sells the TV at 12% loss and the DVD at 15% profit then there is no loss or profit. Find the price of the TV and the DVD ?

TV ……………… DVD
CP—–500…………….400
SP—–+15%………… -12%
P = 75…………… L = -48
Total profit = 75 – 48 = Rs. 27
27 *20 = Rs. 540
CP of TV = 500 * 20 = Rs . 10,000
CP of DVD = 400 * 20 = Rs. 8000.

Example #44
A trader marked his goods at such a price that after allowing a discount of 12(1/2) % for cash payment, he makes a profit of 20% . What is the marked price of the good which costs Rs. 210 ?

Required MP = [210 * (100+20)]/(100-12.5) = (210 *120)/87.5 = Rs. 288.

Example #45
An article is sold at 25% profit. Had it been sold at Rs30 less then there would have been a loss of 25%. What was the cost price (in Rupees)?

Profit = 25% = 1/4
CP………….SP
4………………5
Loss 25%= CP SP
. 4…..3
In both SPs, difference = 5-3 = 2
2=30
1=15
4=60

Example #46
Even after reducing the marked price of a fan by Rs64, a shopkeeper makes a profit of 15%. If the cost price of fan is Rs640 what percent of profit would have been made if he had sold the fan at the market
price?

CP…………SP
20…………23
640……….736
M.P = 736+64 = 800
Profit % = 160/640* 100 = 25%.

Example #47
A man gets a profit of 28% after allowing discount of 11(1/9)%. Find how much percent the cost price should be increased to make this Mark Price?

Gain – 28% CP………SP
. 100………128
Discount 11(1/9)% = 1/9
MP………..SP
9…………….8
Make SP same
CP…………SP…………….MP
100……….128……………144
MP – CP = 44%.

Example #48
A businessman sells a commodity at 10% profit. If he had bought it 10% less and sold it for Rs.2 less, then he would have gained
16(2/3)%. What is the cost price of the commodity?

10% profit = 1/10. So CP = 10, SP = 10+1
= 11
Now make CP 10% less, CP becomes = 9,
Now there is 16(2/3)% profit So SP
becomes 21/2
Original SP = 11, final = 21/2. Difference
is ½
So 1/2 == 2 [Rs 2 less]
1 == 4
and 10 == 40.

Example #49
A customer saves Rs400 at the rebate of 20% on market price of an article. If the cost price of the article for shopkeeper is Rs1200.Then find the profit percent of shopkeeper?

20% of M.P = 400
M.P = 2000
S.P = 1600
C.P= 1200
Profit % = 400/1200* 100= 33(1/3)%.

Example #50
A trader wants to increase his cost price in such a way that after giving 25% discount he earns 20%profit. Find how much percent
he increases his Cost Price?

discount=25% =1/4
MP: SP=4:3
Profit=20%=1/5
CP:SP= 5:6
make ratio equal
MP:CP:SP=8:5:6
=3/5×100=60%.

Example # 51
After selling 12 bat a man suffer a loss equal to cost price of 6 bat. Find loss percent?

loss = CP-SP
CP of 6 bat = CP of 12 bat – SP of 12 bat
SP of 12 bat = CP of 6 bat
Loss % = 6/12*100= 50%.

Example # 52
A women saves Rs.400 at the rebate of 20% on market price of an article. If the cost price of the article for shopkeeper is Rs.1200. Find the profit percent of shopkeeper?

20% of M.P = 400
M.P = 2000
S.P = 1600
C.P= 1200
Profit % = 400/1200x 100= 33(1/3)%.
the profit percent of shopkeeper 33(1/3)%.

Example # 53
A Company wants to increase cost price of a item in such a way that after giving 25% discount he earns 20%profit. Find how much percent he increases his Cost Price?

discount = 25% = 1/4
MP: SP
= 4:3
Profit = 20% = 1/5
CP:SP
= 5:6
make ratio equal
MP:CP:SP
= 8 : 5 : 6
= 3/5×100
= 60%.
He increases his Cost Price 60%.

Example # 54
By selling 20 item, a person gains CP of 5 item. Find the profit% incurred by him.

Profit = SP – CP
CP of 5 item
= SP of 20 item – CP of 20 item
So, CP of 25 item = SP of 20 item
Profit% = 5/20 x 100
= 25%.
25% profit incurred by him.

Example # 55
After selling a sound system worth Rs 12000 at 20% loss, a trader buys a sound system with the same money. Next he sold the sound system at 20% profit. What is his profit/loss in the whole transaction?

12000 – 2400 (20% loss) = 9600
9600 + 1920 (20% profit on 9600) = 11520
So 12000 – 11520 = Rs.480 loss.
His Rs.480 loss in the whole transaction.

Example # 56
A sold a Cycle to B at 10% loss. B sold it to C at 11.11% loss and c again sold it to A at 12.5% profit. How much profit/loss % is incurred by A?

A to B to C
A to B 10% loss, 10% = 1/0.
So, SP for A = 10-1 = 9
B to C 11.11% loss, 11.11% = 1/9, so SP
for B = 9-1 = 8
C to A 12.5% profit, 12.5% = 1/8, so SP for
C or CP for A = 1+8 = 9
A first sold to B at 9, and after he got from
C at 9, so no profit no loss.

Example #57
A watch his profit % on the selling price whereas B watch his on the cost price. They find that the difference of their
profit is Rs 150. If the selling price of both of them are same and both of them get 20% profit, find their selling price (in rupees).

Let SP is x
A’s profit =Xx20/120=X/6
B’s profit =Xx20/100=X/5
Diff isX/6 -X/5=150
X/30=150==>X=4500.

Example #58
A reputed company sells a calculator to a wholesaler making a profit of 10%. The wholesaler, in turn, sells it to the retailer making a profit of 10%. A customer purchases it by paying Rs. 990. Thus the profit of retailer is 2(3/11)% What is the cost (in rupees) incurred by the the company to produce it?

X x 110/100×110/100x(100 + 25/11)/100 = 990
x = 800.

Example #59
A boy sold an electronic watch at Rs.96 in such a way that his percentage profit is same as the cost price of the watch . If he sells it at twice the percentage profit of its previous percentage then find the new selling price.

SP = X + (X x X)/100 = 96%
=> X = 60
New , SP = 60+(60×120)/100
= Rs. 132.

Example #60
A seller procures 40 books for Rs. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

CP = Rs. 3200/40 = Rs.80
Now SP of 40 books = CP of 40 books + SP of 8 books
=> SP of 32 books = 3200
SP of 1 book = Rs.100
Therefore,Required SP of 1 dozen books
= Rs. 1200.

Example #61
A trader has 600kgs of rice ,a part of which he sells at 15% profit and the remaining quantity at 20% loss. On the whole , he incurs an overall loss of 6% .What is the quantity of rice he sold at 20% loss?

Quantity
of rice sold at 20% loss = X kg
(let) Quantity of rice sold at 15% gain
= (600 – X ) kg (600 – X) x (115/100) + (X x80)/100
= (600 x 94)/100
=> X = 12600/35
= 360 kg.

Example #62:
A trader wants to increase his cost price in such a way that after giving 25% discount he earns 20%profit. Find how much percent he increases his Cost Price?
discount=25% =1/4
MP: SP=4:3
Profit=20%=1/5
CP:SP= 5:6
make ratio equal
MP:CP:SP=8:5:6
=3/5×100=60%

Example #63:
A person sold an article at 16 (2/3)% profit on Selling Price. Afterwards when the cost price reduced by 10% then he also reduced the selling price by 10%. His percentage of profit on cost price will be?

Profit on SP= 1/6
SP:CP=6:5 multiply by 10 for easy
calculation= 60:50
60-6 : 50-5=54:45
=(54-45)/45×100=20%

Example #64:
After selling a table worth Rs 12000 at 20% loss, a trader buys a TV with the same money. Next he sold the TV at 20% profit. What is his profit/loss in the whole transaction?
12000 –2400 (20% loss) = 9600
9600 + 1920 (20% profit on 9600) = 11520
So 12000 – 11520 = 480 Rs loss

Example #65:
A shopkeeper sold his articles at cost price. But he used false weights and gives 800 gm instead of 1 kg. Find his profit%.
CP of 1000 gm = SP of 800 gm
So gain% = (1000-800)/800 x 100 = 25%

Example #66:
After selling an article at some price, a trader gain 20% on the selling price. Find his profit% on the cost price.
Profit = 20% on SP
20% = 1/5, (1 – profit, 5 – SP)
CP = SP – Profit 4 = 5 – 1
so, profit% on CP = profit/CP x 100 = 1/4 x 100 = 25%

Example #67:
By selling 20 articles, a person gains CP of 5 articles. Find the profit% incurred by him.
Profit = SP – CP
CP of 5 articles = SP of 20 article – CP of 20 articles
So, CP of 25 articles = SP of 20 articles
Profit% = 5/20 x 100 = 25%.

Example #68:
A boy X sold an Item to Y at 40% loss, then Y sold it to third boy Z at 40% profit and finally Z sold it back to X at 40%
profit. In this whole process what is the percentage loss or profit of X?

Let the CP = Rs.100. for X.
Y’s CP = Rs.60.
Z’s CP = Rs.84.
Finally, X’s CP = Rs.117.6.
So, X’s loss = 117.6 – 60 = Rs.57.6
So, X’s loss percent = 57.6%.

Example #69:
A hole seller sells Marker at the rate of Rs.35 each and earns a commission of 10%. He also sells Gel pen at the rate of
Rs. 65 each and earns a commission of 20%. How much amount (in rupees) of commission will he earn in 2 weeks, if he  sells 12 markers and 8 Gel pens a day?

Commission for
marker=(35×12)x10/100=42
Commission for Gel pen
=(65×8)x20/100=104
Total Commission earned in 2 weeks is,
(104+42)x14=2044.

Example #70:
A shopkeeper allowed a discount of 25% on marked price of Rs.20,000 on an article and incurred a loss of 20%. What discount should he allow on the marked price so that he gains Rs.450 on the article?

25% discount==>20,000×75/100=15000
Then loss 20% means
X x 80/100=15000=3750×5=18750
He gain 450 means SP=18750+450=19200
Now 20000-19200=800
%ge =800/20000×100=4%.

Example #71:
A pen seller procures 40 pens for Rs. 3200 and sells them at a profit equal to the selling price of 8 pens. What is the selling price of one dozen pens, if the price of each pens is same?

CP = Rs. 3200/40 = Rs.80
Now SP of 40 books
= CP of 40 books + SP of 8 books
= SP of 32 books = 3200
SP of 1 book = Rs.100
So,
Required SP of 1 dozen books
= Rs. 1200.

Example #72:
A trader has 600kgs of sugar ,a part of which he sells at 15% profit and the remaining quantity at 20% loss. On the whole , he incurs an overall loss of 6% .What is the quantity of sugar he sold at 20% loss?

Quantity of sugar sold at 20% loss = x kg
let,
Quantity of sugar sold at 15% gain
= (600 – X ) kg (600–X) x (115/100) + (X x 80)/100
= (600 x 94)/100
= x = 12600/35 = 360 kg.

Example #73:
A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. Find his gain%.

CP = 100 , MP = 120
D = (15/100)x120 = 18%
SP = 102
P% = (P/CP)x100 = (2/100)x100 = 2%.

Example #74:
A shopkeeper bought a DVD marked at Rs. 200 at successive discounts of 10% and 15% respectively. He spent Rs. 7 on transport and sold the table for Rs.208 .What will be his profit percentage ?

Single equivalent discount for 10% and
15% = (15 + 10 – (15×10/100))%
= 23.5%
CP of DVD = 200x(100- 23.5)% = Rs.153
Expense on transport = Rs. 7
Actual CP = 153 + 7 = Rs. 160
Profit % = [(208 – 160)/160]x100 = 30%.

Example #75:
The cost of setting up a magazine is Rs.2800. The cost of paper and ink is Rs.80/ 100 copies and printing cost is Rs. 160 / 100 copies. In the last month 2000 copies were printed but only 1500 copies could be sold at Rs. 5 each . Total 25% profit on the sale price was realized. There is one more resource of income from the magazine which is advertising. What sum of money was obtained from the advertising in magazine?

Setup cost = Rs.2800 Paper , ink = Rs. 1600
Printing cost = Rs. 3200
Total cost = Rs. 7600
Total sale price = 1500×5 = 7500
Let the amount obtained from advertising is x,
then (7500+x) – 7600 = 25% of 7500
x = 1975.

Example #76:
A dealer offers a discount of 20% and still makes a profit of 20% and he further allows 4 articles free on the sale of 12 articles. Find the ratio of cost price to market price.

Formula : MP(1 – d%) = CP(1+g%)
MP(80/100) = CP(120/100)
CP/MP = 80/120———(1)
Now,
16 articles given in the cost of 12 articles
MP of one article = total /12——–(2)
CP of one article = total /16———(3)
For one article:
CP/MP= (80/16)/(120/12) = 1/2.

Example #77:
A bookseller procures 40 books for Rs. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

CP = Rs. 3200/40 = Rs.80
Now SP of 40 books = CP of 40 books +
SP of 8 books = SP of 32 books = 3200
SP of 1 book = Rs.100
Therefore,
Required SP of 1 dozen books = Rs. 1200.

Example #78:
A man buys some toffees at 5 toffee in 3rupee and same number of toffee at 5 toffee in rs4. He sold all of them at 5 toffee in 4 rupee. Find his overall gain or loss percent?
Rs——Qty
3——5
4——5

C.P Rs.7 10 toffees
He sold at 5 toffees in Rs.4
so, for 10 toffees he gets Rs.8 C.P = Rs,27—- S.P = Rs,28 Profit % = 1/7 x 100 = 14(2/7)%.

Example #79:
By selling 144 hens Mahesh suffer a loss equal to the selling price of 6 hens. Find his loss percent?

loss = C.P – S.P
S.P of 6 hen = C.P of 144 hens –S.P of 144 hens
S.P of 150 hens = C.P of 144
hens 6/150 x 100 = 4% loss.

Example #80:
An article is sold at 33(1/3)% profit. If it had been sold at a profit of 40%,it would have fetched Rs50 more. Find cost price of article ?

1st 33(1/3)% profit so CP = 3, and
SP = 3+1 = 4
2nd 40% = 2/5. So CP = 5, SP = 7
Now CP is same so make CP same
CP…… SP
15…… 20
15…… 21
20 to 21 is + 1,
so, 1= 50 [increase in SP]
So, 15=750.

Example #81
A trader wants to increase his cost price in such a way that after giving 25% discount he earns 20%profit. Find how much percent he increases his Cost Price?

discount=25% =1/4
MP: SP=4:3
Profit=20%=1/5
CP:SP= 5:6
make ratio equal
MP:CP:SP=8:5:6
=3/5*100=60%.

Example #82
A shopkeeper allows 2% discount and gives 1 article free on purchase of 6 articles. He earns 40% profit during the transaction. By what percent above the cost price he marked his good.

Discount=2%=1/50 MP:SP=50:49 Profit=40%=2/5=> CP:SP=5:7 MP:SP:CP=50:49:35 This 35 is the CP of (6+1) hence the CP for 6 will be 30 (50-30)/30*100= 66 (2/3)%

Example #83
On selling 15 balls at Rs 400 there is loss equal to Cost Price of 5 balls. The cost price of a ball is?

loss= CP-SP
CP of 5=CP of 15- SP of 15
CP of 10=SP of 15=400
CP of 1 =40.

Example #84
After selling a table worth Rs 12000 at 20% loss, a trader buys a TV with the same money. Next he sold the TV at 20% profit. What is his profit/loss in the whole transaction?

12000 – 2400 (20% loss) = 9600
9600 + 1920 (20% profit on 9600) = 11520
So, 12000 – 11520 = 480 Rs loss.

Example #85
A man bought some toffees at the rate of 3 toffees per Re. and same number at the rate of 2 toffees per Re. He mixes them and sold 3 toffees for Rs 2. Find his profit/loss% in the whole transaction.

Profit is 20%.
So 1000gm + 20% of 1000gm = 1200gm
so, CP of 1200gm = SP of 800gm
Sp profit% = (1200-800)/800 x 100 = 50%.

Example #86
A shopkeeper sold his articles at cost price. But he used false weights and gives 800 gm instead of 1 kg. Find his profit%.

CP of 1000 gm = SP of 800 gm
So, gain% = (1000-800)/800 * 100 = 25%.
So, 12000 – 11520 = 480 Rs loss.

Example #87
After selling a table worth Rs 12000 at 20% loss, a trader buys a TV with the same money. Next he sold the TV at 20% profit. What is his profit/loss in the whole transaction?

12000 – 2400 (20% loss) = 9600
9600 + 1920 (20% profit on 9600) = 11520
So, 12000 – 11520 = Rs.480 loss.

Example #88
After selling an article at some price, a trader gain 20% on the selling price. Find his profit% on the cost price.

Profit = 20% on SP
20% = 1/5, (1 – profit, 5 – SP)
CP = SP – Profit 4 = 5 – 1
so profit% on CP = profit/ CP  x 100 = 1/4 x 100 = 25%.

Example #89
A sold a watch to B at 10% loss. B sold it to C at 11.11% loss and c again sold it to A at 12.5% profit. How much profit/loss % is incurred by A?

A to B to C
A to B 10% loss, 10% = 1/0.
So, SP for A = 10-1 = 9
B to C 11.11% loss, 11.11% = 1/9,
so, SP for B = 9-1 = 8 C to A 12.5% profit, 12.5% = 1/8,
so, SP for C or CP for A = 1+8 = 9
A first sold to B at 9, and after he got from
C at 9, so no profit no loss.

Example #90
On selling 15 balls at Rs 400 there is loss equal to Cost Price of 5 balls. The cost price of a ball is?
loss = CP-SP
CP of 5 = CP of 15- SP of 15
CP of 10 = SP
CP of 1 = 40.

Example 91#
Of the two varieties of rice available, variety A is bought at Rs.32 per kg and variety B at Rs.80 per kg. Two varieties of rice are mixed together in the respective ratio of 8:5 and the mixture is sold at Rs.72 per kg. What per cent of profit approximately the seller receives ?

Let 8 kg of first variety of rice and 5 kg of second variety is mixed. CP of 13 kg of rice = (8×32 + 5×32) = Rs. 656 SP of 13 kg of rice = 72×13 = Rs.936 Profit = 936 – 656 = Rs.280 Profit% = (280/656)x100 = 43%.

Example 92#
A camel and a cart together cost Rs. 5000.If by selling the camel at a profit of 10% and the cart at a loss of 10% a total profit of 2.5% is made ,then what is the cost price of the camel ?

Let the cp of the camel and the cart be X and (8000-X) resp.
sp of camel = 1.1X sp of cart = 0.9(5000-X)
Therefore , 1.1X x 0.9(5000 – X)
= 5000 X 1.025
= X = Rs. 3125

Example 93#
If there is a loss of 40% when a good is sold at (2/5)th of its earlier selling price. Find the profit% after selling the good at a certain price

CP = (2/3) of SP
SP = (100+P) / 100 of CP Equating both the above equations,
Profit = 50%.

Example 94#
An article is marked 50% over its cost price.Two successive discounts of 12% and 13(1/2)% are allowed on the marked price of the article.Find the profit or loss percent after selling at discount.

Let the CP be Rs. 100 SP
= 150 x (88/100) x (86.5/100)
= Rs. 114.18
Therefore , = (14.18/100)x100 =14.18%.

Example 95#
A trader marked his goods at such a price that after allowing a discount of 12(1/2) % for cash payment, he makes a profit of 20% . What is the marked price of the good which costs Rs. 210 ?

Required MP = [210 x (100+20)]/(100-12.5)
= (210 x 120)/87.5
= Rs. 288.

Example 96#
A sold an article to B at the profit of 25%, B sold it to C at loss of 10% and C sold it to D at the profit of 20%. If D paid rs27, then how much A paid to buy this article?

125/100 x 90/100 x 120/100 x X
= 27 X = rs20.

Example 97#
If 8kg of tea price costing Rs56/kg is blended with 32kg of tea of Rs69/kg and 25kg of Rs75/kg and the mixture is sold at 20% profit. Find the selling price (in rupees) of mixture?

(8×56 + 32×69 + 25×75)/ 65
= 69.70 (69.70/100) x 120
= 83.64.

Example 98#
The price of coal is increased by 20%. By what percent a family should decrease its consumption so that expenditure remains same?

increased 20% = 1/5 Since there is increase,
so, decrease in consumption will be 1/(5+1) = 1/6 = 16 2/3% In there was decrease,
so, increase in consumption would have been 1/(5-1)
= 1/4 = 25%.

Example 99#:
A shopkeeper sold his articles at cost price. But he used false weights and gives 800 gm instead of 1 kg. Find his profit%.

1. 