Profit and Loss

22 comments
Profit and Loss

The terms Profit and Loss are used in businesses. In business transactions, goods are purchased and sold. The price used to purchase is called “Cost Price” and written as CP. The price obtained by selling goods is called “Selling Price” and it is written as SP.



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If the selling price of certain item is more than the cost price, then there is a profit. If the cost price of certain item is more than its selling price, then there is a loss. For example:


-    An article is bought for Rs. 500 and sold it for Rs. 600. Here, SP is more than CP, so there is a profit of Rs. 600 – 500 = Rs. 100


-    An article is bought for Rs. 1000 and sold for Rs. 800. Here, CP is more than SP, so there is a loss of Rs. 1000 – 800 = Rs. 200


As stated in the examples above,


If SP>CP, there is a profit and it is obtained as


Profit (P) = SP – CP



If CP>SP, there is loss and it is obtained as


Loss (L) = CP – SP

Profit and loss percent is calculated on the basis of cost price (CP). So,


Profit percent (P%) = Profit/CP × 100%. Loss percent (L%) = Loss/CP × 100%


The formula of CP, SP, Profit, and Loss:


1. Profit = SP – CP 2. Loss = CP – SP 3. SP = CP + Profit 4. CP = SP – Profit 5. SP = CP – Loss 6. CP = SP + Loss 7. Profit percent (P%) = Profit/CP × 100% 8. Loss percent (L%) = Loss/CP × 100% 9. CP = 100/(100 + P%) × SP 10. CP = 100/(100 - L%) × SP 11. SP = (100 + P%)/100 × CP 12. SP = (100 - L%)/100 × CP


How to solve the problems related to Profit and Loss?


While solving the problems related to profit and loss we must use the following steps:


i.     Understand the problem and make planing.

ii.    Solve problem according to the planing.

iii.  Review solved problem and recheck  it.

iv.  At last, write the conclusion according to the question.

Worked Out Examples


Example 1: Mrs. Sarala bought a Banarasi Sari at Rs 3500. After one month, she was interested to have a new one and hence she sold it for Rs. 3200. Find her loss percent.


Solution: Here,


CP = Rs. 3500, SP = Rs. 3200 ∴ Loss = CP – SP = Rs. 3500 – 3200 = Rs. 300 ∴ Loss percent = Loss/CP × 100% = 300/3500 × 100% = 8.57%


∴  Her loss percent is 8.57%.



Example 2: Sabin bought 14 copies for Rs. 140 and sold 8 copies for Rs. 96. Find his profit or loss percent.


Solution: Here,


CP of 14 copies = Rs. 140 ∴ CP of 1 copy = Rs. 140/14 = Rs. 10 SP of 8 copies = Rs. 96 ∴ SP of 1 copy = Rs. 96/8 = Rs. 12 ∴ For 1 copy, SP > CP. So there is profit. ∴ Profit = SP – CP = Rs. 12 – 10 = Rs. 2 ∴ Profit percent = Profit/CP × 100% = 2/10 × 100% = 20%


∴ He has got a profit of 20%.



Example 3: An exercise book cost Rs. 20. If it is sold at a profit of 10%, find its selling price.


Solution: Here,


CP = Rs. 20, Profit = 10%, SP = ? We know, SP = (100 + P%)/100 × CP = (100 + 10)/100 × 20 = 110/100 × 20 = Rs. 22


∴  The selling price of that exercise book is Rs. 22.

Example 4: If a shopkeeper sells a shirt for Rs. 270 at a loss of 10%, for what price should it be sold, so as to get a gain of 30%?


Solution: Here,


1st Case, SP = Rs. 270, Loss = 10% ∴ CP = 100/(100 - L%) × CP = 100/(100 - 10) × 270 = 100/90 × 270 = Rs. 300 2nd Case, CP = Rs. 300, Profit = 30% ∴ SP = (100 + P%)/100 × CP = (100 + 30)/100 × 300 = 130/100 × 300 = Rs. 390


∴ The shirt should be sold at Rs 390 to get a profit of 30%.



Example 5: Salman sold a DVD at a gain of 8%. Had it been sold for Rs. 75 more, the gain would have been 14%. Find the cost price of the DVD.


Solution: Here,


Let, CP = Rs. x ∴ SP1 at 8% gain = (100 + P%)/100 × CP = (100 + 8)/100 × x = 108x/100 ∴ SP2 at 14% gain = (100 + 14)/100 × x = 114x/100 According to question, SP2 – SP1 = Rs. 75 i.e. 114x/100 – 108x/100 = 75 or, (114x-108x)/100 = 75 or, 6x/100 = 75 or, 6x = 7500 or, x = 7500/6 or, x = 1250


Hence, the CP of the DVD is Rs. 1250.



Do you have any questions regarding the Profit and Loss?

You can ask your questions or problems in the comment section below.

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About author: Min Rajbanshi

I am a school math teacher and a blogger since 2012. I do blogging on a variety of topics including math. Over the years, I've explored and written about a wide range of topics, with a particular emphasis on mathematics. My passion for education extends beyond the classroom, as I enjoy sharing knowledge and insights on various subjects through my blog.

22 comments:

  1. UnknownOctober 18, 2021 at 9:35 AM

    A man allows a discount of 10% on a book whose marked price is ₹40. What is the cost price so that the profit is 20% ?

    ReplyDelete
    Replies
    1. Min RajbanshiOctober 20, 2021 at 7:34 AM

      Solution: Here,
      MP = ₹40
      Discount = 10%

      SP = (100 – d%)MP/100 = (100 – 10)40/100 = 90×40/100 = ₹36
      Profit = 20%

      CP = 100SP/(100+P%) = 100×36/(100+20) = 3600/120 = ₹30

      ∴ The cost price is ₹30. Ans.

      Delete
  2. UnknownJanuary 23, 2022 at 8:54 AM

    price of a pen is 240 with discount perfect of 5%. What amount shoult be paid when discount would be 10%?

    ReplyDelete
    Replies
    1. Min RajbanshiJanuary 23, 2022 at 10:50 PM

      Solution: Here,
      1st Case,
      SP = 240
      Discount = 5%
      MP = [100/(100-d%)] × SP = [100/95] × 240 = 252.63
      2nd Case,
      MP = 252.63
      Discount = 10%
      SP = [(100-d%)/100] × MP = [90/100] × 252.63 = 227.36

      ∴ 227.36 should be paid.

      Delete
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  4. UnknownFebruary 19, 2022 at 2:56 AM

    An article was sold for 10% discount there is a profit of 5%.if the same article is sold at 5% discount there will be Rs 251 profit.find the marked price and cost price

    ReplyDelete
    Replies
    1. Min RajbanshiFebruary 20, 2022 at 8:29 AM

      Solution:
      Here,
      MP = Rs. x (let)

      1st Case,
      Discount = 10%
      ∴ SP = (100-d%)/100 × MP = 90x/100
      Profit = 5%
      ∴ CP1 = 100/(100+P%) × SP = 6x/7

      2nd Case,
      Discount = 5%
      ∴ SP = (100-d%)/100 × MP = 19x/20
      Profit = Rs. 251
      ∴ CP2 = SP – Profit = 19x/20 – 251

      But, CP is the same,
      ∴ CP1 = CP2
      i.e. 6x/7 = 19x/20 – 251
      or, 6x/7 = (19x – 5020)/20
      or, 120x = 133x - 35140
      or, 120x – 133x = – 35140
      or, -13x = -35140
      or, x = -35140/-13
      or, x = 2703.07

      ∴ MP = x = Rs. 2703.07
      ∴ CP = 6x/7 = Rs. 2316.90

      Delete
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  6. UnknownMarch 7, 2022 at 9:30 AM

    A man bought two school bags for RS.2020.He sold one of them at 20% profit and the other at 20% loss.Find his gain or loss percent in this transaction if the selling prices of both bags are same.

    ReplyDelete
    Replies
    1. Min RajbanshiMarch 7, 2022 at 6:55 PM

      Solution: Here,
      Total CP = Rs. 2020

      For 1st bag,
      CP = Rs. x (let)
      Profit = 20%
      ∴ SP = (100+P%)CP/100 = (100+20)x/100 = 120x/100 = 6x/5

      For 2nd bag,
      CP = Rs. 2020 – x
      Loss = 20%
      ∴ SP = (100 – L%)CP/100 = (100 – 20)(2020 – x)/100 = (8080 – 4x)/5

      Both the SP are same,
      ∴ 6x/5 = (8080 – 4x)/5
      Or, 6x = 8080 – 4x
      Or, 6x + 4x = 8080
      Or, 10x = 8080
      Or, x = 8080/10
      Or, x = 808

      ∴ Total SP = 2×6x/5 = 2×6×808/5 = Rs. 1939.2

      CP > SP, so there is loss.
      ∴ Loss = SP – CP = Rs. 1939.2 – 2020 = Rs. 80.8

      ∴ Loss % = Loss × 100/CP = 80.8×100/2020 = 4%

      Delete
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  9. susantNovember 5, 2022 at 2:14 AM

    A shopkeeper adds 30% on the cost price of any article for m.p and sells allowing 10% discount . If his cost price for an article is Rs 24000 then find its actual selling price.

    ReplyDelete
    Replies
    1. Min RajbanshiNovember 5, 2022 at 6:43 AM

      Solution:
      Here,
      CP = Rs. 24000
      MP = CP + 30% of CP = Rs. 24000 + (30/100) × 24000 = Rs. 31200
      Discount = 10%

      Actual SP = MP – Discount
      = Rs. 31200 – 10% of 31200
      = Rs. 31200 – (10/100) × 31200
      = Rs. 28080 Ans.

      Delete
  10. susantNovember 5, 2022 at 2:18 AM

    Ananta purchased one scocetage peroter at Rs 65000 and other at Rs.75000. Find his profit and loss percentage if he sold both at the rate of Rs. 72000 each.

    ReplyDelete
    Replies
    1. Min RajbanshiNovember 5, 2022 at 6:44 AM

      Solution:
      Here,
      Total CP = Rs. 65000 + 75000 = Rs. 140000
      Total SP = Rs. 72000 × 2 = Rs. 144000

      SP > CP, so there is profit,

      Profit = SP – CP = Rs. 144000 – 140000 = Rs. 4000

      Profit % = (Profit/ CP) × 100%
      = (4000/140000) × 100%
      = 2.85% Ans.

      Delete
  11. susantNovember 5, 2022 at 2:20 AM

    A shopkeeper allows a discount of 10% on the marked price , he still makes a gain of 12.5%. By what percent the marked price above the cost price.

    ReplyDelete
    Replies
    1. Min RajbanshiNovember 5, 2022 at 6:44 AM

      Solution:
      Here,
      MP = x (let)
      Discount = 10%
      SP = MP – Discount = x – 10% of x = x – 10x/100 = 90x/100
      Profit = 12.5%

      CP = (100/100 + P%) × SP = (100/100+12.5) × 90x/100 = 90x/112.5

      Percent above = (MP – CP)×100%/CP
      = (x – 90x/112.5)×100%/(90x/112.5)
      = 2250x/90x
      = 25% Ans.

      Delete
  12. Awadesh Prasad KurmiAugust 12, 2023 at 6:31 AM

    A TV was sold at Rs. 43200 by adding 20% VAT after 10% discount. What is the
    discount allowed on the TV ?

    ReplyDelete
    Replies
    1. Min RajbanshiAugust 12, 2023 at 7:03 AM

      Solution:
      Here,
      SP with VAT = Rs. 43200
      Discount = 10%
      VAT = 20%

      By formula,
      MP = 100×100×SP with VAT /(100-d%)(100+v%)
      = 100×100×43200/(100-10)(100+20)
      = 432000000/90×120
      = Rs. 40000

      Now,
      Discount = 10% of MP
      = 10×40000/100
      = Rs. 4000

      Delete
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