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# Maths : Profit & Loss (Solved in Steps)

1. Aravind buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, what is his gain percent?

A. 12%

B. 10%

C. 44.7%

D. 5.45 %

Answer : Option D

Explanation :

Cost Price (CP) = 4700 + 800 = Rs. 5500
Selling Price (SP) = Rs. 5800.
Gain = (SP) – (CP) = 5800 – 5500= Rs. 300.
Gain%
= (GainCP)×100
= (300÷5500)×100
= 300÷55
= 60÷11
= 5.45

2. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x

A. 15

B. 25

C. 18

D. 16

Answer : Option D

Explanation :

Let the Cost Price (CP) of one article = 1
=> CP of x articles = x ——————————( 1)
CP of 20 articles = 20
Given that cost price of 20 articles is the same as the selling price of x articles
=> Selling price (SP) of x articles = 20————–( 2)
Given that Profit = 25%
(SP-CP)÷CP
=25÷100=1/4————( 3)
Substituting equations 1 and 2 in equation 3,
⇒(20-x) ÷x = 1/4
⇒80-4x=x
⇒ 5x=80
⇒ x=80÷5
=16

3. If the selling price is doubled, the profit triples. What is the profit percent?

A. 100

B. 105.33

C. 66.66

D. 120

Answer : Option A

Explanation :

Let the CP = x , SP = y
profit = SP –CP = y-x
If SP is doubled, SP = 2y
Now Profit = SP –CP = 2y – x
Given that If selling price is doubled, the profit triples
⇒2y–x=3(y-x)
⇒2y–x=3y-3x
⇒y=2x
⇒Profit%=(Profit÷CP)×100
=((y-x)÷x)×100
=((2x–x)÷x)×100
=(x÷x)×100=100%

4. In a shop, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, find out approximately what percentage of the selling price is the profit?

A. 250%

B. 100%

C. 70%

D. 30%

Answer : Option C

Explanation :

Let the CP = 100
Profit=(320÷100)×100
=320
SP=CP+Profit=100+320=420
If the cost increases by 25%,
New CP=(125÷100)×100=125
Selling Price is constant, hence New SP=420
Profit=SP–CP=420–125=295
Required Percentage =(295÷420)×100
=2950÷42
=70(approximately)

5. Sebastian bought bananas at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A. 3

B. 4

C. 5

D. 6

Answer : Option C

Explanation :

CP of 6 bananas = 1
Gain = 20%
SP of 6 bananas=1×(120÷100)
=12÷10
⇒The number of bananas he should sell for Rs.1 for
a gain of 20%
=(10÷12)×6
=10÷2=5

6. An exporter expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

A. Insufficient Data

B. Rs. 80

C. Rs. 90

D. Rs. 72

Answer : Option D

Explanation :

SP=392
Gain=22.5%
CP=(100÷(100+Gain%))×SP
=(100÷(100+22.5))×392
=(100÷122.5)×392
=(1000÷1225)×392
=(40÷49)×392
=(40÷7)×56
=40×8
=320
Profit=SP-CP=392-320=7

7. The percentage profit earned by selling an item for Rs. 1920 is equal to the percentage loss incurred by selling the same item for Rs. 1280. At what price should the item be sold to make 25% profit?

A. Insufficient Data

B. Rs. 3000

C. Rs. 2000

D. Rs. 2200

Answer : Option C

Explanation :

Let CP = x
Percentage profit earned by selling an item for Rs. 1920
= ( (SP-CP)÷CP)×100
= ((1920-x)÷x)×100
Percentage loss incurred by selling the same item for Rs. 1280
=((SP-CP)÷CP)×100= ((x-1280)÷x)×100
Given that Percentage profit earned by selling an item for Rs. 1920=Percentage loss incurred by selling the same item for Rs. 1280
⇒((1920-x)÷x)×100=((x-1280)÷x)×100
⇒(1920-x)÷x=(x-1280)÷x
⇒ 1920–x = x–1280
⇒2x=1920+1280=3200
⇒ x=3200÷2=1600
Required Selling Price=CP×(125÷100)
=1600×(125÷100)=1600×(5÷4)=400×5=2000

8. A man buys a scooter for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the scooter?

A. Rs. 1240

B. Rs. 1190

C. Rs. 1090

D. Rs. 1130

Answer : Option B

Explanation :

SP=1400×(85÷100)=14×85=1190

9. Murali purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. Find out his profit percentage?

A. 3.5

B. 5.6

C. 4.1

D. 3.4

Answer : Option B

Explanation :

CP of 1 toy=(375÷12)
SP of 1 toy=33
Profit=SP-CP
=33-(375÷12)
Profit%=(Profit÷CP)×100
={(33-(375÷12)) ÷(375÷12)}×100
=(33×(12÷375)-1)×100
=(33×(4÷125)-1)×100
=(7÷125)×100
=(7÷5)×4
=28÷5
=5.6%

10. Some items were bought at 6 items for Rs. 5 and sold at 5 items for Rs. 6. What is the gain percentage?

A. 44%

B. 3313

C. 3123

D. 30%

Answer : Option A

Explanation :

CP of 1 item=5÷6
SP of 1 item=6÷5
Gain%=((SP-CP)÷CP)×100
={((6÷5)-(5÷6)) ÷(5÷6)}×100
={(36÷25-1)}×100
=(11÷25)×100
=11×4=44

11. 100 oranges were bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. What is the percentage of profit or loss?

A. 11.29% Loss

B. 11.14% Profit

C. 14.29% Profit

D. 14.29% Loss

Answer : Option C

Explanation :

CP of 100 oranges=350
⇒CP of 1 orange=350÷100=3.5
SP of 12 oranges=48
⇒SP of 1orange=48÷12=4
Profit%={(SP-CP)÷CP}×100
={(4-3.5)÷3.5}×100= (.5÷3.5)×100=(1÷7)×100=100÷7=14.29

12. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. What is the cost price of a ball?

A. Rs. 43

B. Rs. 60

C. Rs. 55

D. Rs. 34

Answer : Option B

Explanation :

Loss = (CP of 17 balls) – (SP of 17 balls) = (CP of 17 balls) – 720
Given that Loss = (CP of 5 balls)
=> (CP of 17 balls) – 720 = (CP of 5 balls) => (CP of 17 balls) – (CP of 5 balls) = 720
=> CP of 12 balls = 720
=> CP of 1 ball=720÷12=60

13. When an item is sold for Rs. 18,700, the owner loses 15%. At what price should that plot be sold to get a gain of 15%?

A. Rs. 25100

B. Rs. 24200

C. Rs. 25300

D. Rs. 21200

Answer : Option C

Explanation :

When an item is sold for Rs. 18,700, the owner loses 15%⇒SP = 18700 and Loss=15%
⇒CP={100÷(100 -Loss%)}×SP
={100÷ (100″15)}×18700={100÷85}×18700
To get a gain of 15%, SP ={(100+Gain%)÷100}×CP
={(100+15)÷100}×CP
=(115÷100)×CP
={(115÷100)×(100÷85)}×18700=(115÷85)×18700=(23÷17)×18700
=23×1100=25300

14. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. What is his profit percentage?

A. 6%

B. 5%

C. 4%

D. 7%

Answer : Option B

Explanation :

CP of 1st variety rice=20
CP of 2nd variety rice=36
CP of the 56 kg rice mixture=(26×20+30×36)=520+1080=1600
SP of the 1 kg rice mixture=30
SP of the 56 kg rice mixture=30×56=1680
Gain=SP-CP=1680-1600=80
Gain%=(Gain÷CP)×100=(80÷1600)×100=5%

15. If a material is sold for Rs.34.80, there is a loss of 25%. Find out the cost price of the material?

A. Rs.46.40

B. Rs.44

C. Rs.42

D. Rs.47.20

Answer : Option A

Explanation :

SP=34.80
Loss=25%
CP={100÷ (100-Loss%)}×SP
=[100÷ (100-25)]×34.80=(100÷75)×34.80
=[4×34.80]÷3
=4×11.60=46.40

16. By selling an item for Rs.15, a trader loses one-sixteenth of what it costs him. The cost price of the item is?

A. Rs.14

B. Rs.15

C. Rs.16

D. Rs.17

Answer : Option C

Explanation :

SP=15
Loss=CP÷16
Loss=CP-SP=CP-15
⇒(CP÷16)=CP-15
⇒(15 CP÷16)=15
⇒(CP÷16)=1
⇒CP=16

17. A fruit seller sells apples at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?

A. 11.32

B. 11

C. 12

D. 11.81

Answer : Option D

Explanation :

SP=9
Loss=20%
CP={100÷ (100-Loss%)}×SP={100÷ (10020)}×9={100÷80}×9=(5÷4)×9
To make a profit of 5%,
SP={(100+Gain%)÷100}×CP=[(100+5)
÷100]×CP
=(105÷100)×((5÷4)×9)=
=((21÷20)×(5÷4)×9)= 11.81

18. A trader gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the labelled price of an item. The final sale price of the item is Rs.704. Find out the labelled price?

A. 1000

B. 2000

C. 1200

D. 920

Answer : Option A

Explanation :

Let the labelled price=x
SP=704
Initial Discount=20%
Price after initial discount=x×(80÷100)
Price after additional discount=x×(80÷100)×(88÷100)
But Price after additional discount=SP=704
⇒x×(80÷100)×(88÷100)=704
⇒x×(4÷5)×(22÷25)=704
⇒x=704×(25÷22)×(5÷4)= 1000

19. John purchased a machine for Rs. 80,000. After spending Rs.5000 on repair and Rs.1000 on transport he sold it with 25% profit. What price did he sell the machine?

A. Rs.107000

B. Rs.107500

C. Rs.108500

D. None of these

Answer : Option B

Explanation :

CP=80,000+5000+1000=86000
Profit=25%
SP=[(100+Gain%)÷100]×CP
=[(100+25)÷100]×86000
=(125÷100)×86000
=(5÷4)×86000=5×21500=107500

20. A shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight. What is his profit percentage?

A. 18%

B. 40%

C. 25%

D. 20%

Answer : Option C

Explanation :

If a trader professes to sell his goods at cost price but uses false weights, then
Gain%=[(Error÷ (True Value-Error))×100]%
So here profit percentage=[(200÷ (1000200))×100]%
=[(200÷800)×100]%=25%

21. An item was sold for Rs.27.50 with a profit of 10%. If it was sold for Rs.25.75, what would have been the percentage of profit or loss?

A. 3%

B. 2%

C. 4%

D. 5%

Answer : Option A

Explanation :

SP = 27.5
Profit = 10%
CP=[100÷ (100+Profit%)]×SP
=[100÷(100+10)]×27.5
=2750÷110=25
If the item was sold for Rs.25.75,
Gain%=[(25.75-25) ÷25]×100=[0.75÷25]×100=3%

22. Prasanth bought a car and paid 10 % less than the original price. He sold it with 30% profit on the price he had paid. What percentage of profit did he earn the original price?

A. 17%

B. 16%

C. 18%

D. 14%

Answer : Option A

Explanation :

Let the original price=100
Then the price at which he purchased (CP) =90% of
100=90
Profit=30%
SP=((100+Profit%)÷100)×CP
=[(100+30)÷100]×90
=[130÷100]×90=13×9=117
Required %=[(117-100) ÷100]×100=17%

23. If a seller reduces the selling price of an item from Rs.400 to Rs.380, his loss increases by 2%. What is the cost price of the item?

A. 1000

B. 800

C. 1200

D. 1100

Answer : Option A

Explanation :

Initial Loss% = {[ CP-400] ÷CP}×100
If the SP is reduced from 400 to 380, Loss% = [ (CP380)÷CP]×100
It is given that If the SP is reduced from 400 to 380,
Loss% increases by 2
⇒[(CP-380)÷CP]×100- {[ CP-400] ÷CP}×100=2
⇒(CP-380)-(CP-400)=2×[CP÷100]
⇒20=2×[CP÷100]
⇒CP=(20×100)÷2=1000

24. If the selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price

A. 5: 3

B. 3 : 5

C. 4 : 5

D. 5 : 4

Answer : Option C

Explanation :

SP = 250
Profit = 25%
CP=[100÷ (100+Profit%)]×SP
=[100÷ (100+25)]×250==[100÷125]×250=200
Required Ratio = 200 : 250 = 4:5

25. Sunil purchases two books at Rs.300 each. He sold one book 10% gain and other at 10% loss. What is the total loss or gain in percentage?

A. 10% gain

B. 1% loss

C. No loss or no gain

D. 1% gain

Answer : Option C

Explanation :

CP of two books = 300 + 300 = 600
SP of two books
= 300×(110÷100)+300×(90÷100)=(300÷100)×(110+90)=3×200=600
Total SP = Total CP
Hence No loss or no gain