Note on Profit and Loss

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The producerproduces a goods at some certain cost. When those goods are sold at a higher price than the production price, then there is profit. And, if the goods are sold at lower price than production cost, then he suffers a loss.

Thus, profit = Selling price - Cost price

or,Profit = S.P - C.P

Loss = Cost Price - Selling Price

or, Loss= C.P - S.P

For example:

If Renu bought a book for Rs 500 and sold it for Rs 600, then she made a profit of Rs 100 i.e profit = Rs 100

Similarly, if Ritesh bought a machine for Rs 200 and sold it for Rs 100, then he suffered a loss of Rs 100. i.e loss = Rs 200 - Rs 100 = Rs 100 (loss)

Profit Percentage and Loss Percentage

 

z

 

 

x

 

For the purpose of comparison, we usually express the actual profit or loss as a percentage of a cost price.

For example; Samikshya sold a bag for Rs 60 which costs Rs 50 and shoes sold for Rs 110 which costs Rs 100. In each case, the shopkeeper makes a profit of Rs 10. It seems that in both cases profit is equally gained.

But in percentage we have:

In the first case, profit percentage = \(\frac{10}{ 50}\) x 100 = 20 %

In the second case, profit percent = \(\frac{10}{100}\) x 100 = 10 %

Hence, in the first case, she made more profit than in the second case, it is better and accurate method of comparison.

Have a look at these formulas:

Percentage profit = \(\frac{actual\;profit}{C.P}\) x 100

Percentage loss = \(\frac{actual\;loss}{C.P}\) x 100

Examples

  1. A pen costing Rs 28 sold for RS 36. Find the percentage profit.
    Solution:
    Cost price (CP) = RS 28
    Selling price(SP) = Rs 35
    Actual profit = SP - CP = Rs 35 - Rs 28 = Rs 7
    Percentage profit= \(\frac{actual \;profit}{CP}\)×100 =\(\frac{7}{28}\)×100 =25%

  2. A book costing Rs 60 sold for Rs 50. Find the percentage loss.
    Solution:
    Cost price (CP) = Rs 60
    Selling price (SP) = Rs 50
    Actual loss = CP - SP = Rs 60 - Rs 50 = Rs 10
    Percentage loss = \(\frac{actual \;loss}{CP}\)×100 =\(\frac{10}{60}\)×100 =16\(\frac{2}{3}\)%

  • The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
  • The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
  • If S.P. is greater than C.P., the seller is said to have a profit or gain.
  • If S.P. is less than C.P., the seller is said to have incurred a loss.
  • Loss or gain is always reckoned on C.P.

 

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Very Short Questions

Solution:

Given information,

Cost Price (CP) = Rs 28

Selling Price (SP) = Rs 35

Here,

Actual Profit = SP - CP = Rs 35 - Rs28 = Rs 7

Now,

Percentage Change = \(\frac{actual profit}{CP}\) × 100

= \(\frac{7}{28}\)× 100

= 25%

Solution;

Given information,

Cost Price (CP) = Rs 60

Selling Price (SP) = Rs 50

Here,

Actual Loss = CP - SP

= Rs 60 -Rs 50

= Rs 10

Now,

Percentage Loss = \(\frac{actual loss}{CP}\)× 100

= \(\frac{10}{60}\)×100

= 16 \(\frac{2}{3}\) %

Solution:

Let the cost price be Rs x.

Then, profit = 30% of x

= \(\frac{30}{100}\)× x

= \(\frac{3x}{10}\)

Now,

CP = SP - Profit

or, x = 65 - \(\frac{3x}{10}\)

or, x + \(\frac{3x}{10}\) = 65

or, \(\frac{10x+3x}{10}\) = 65

or, 13x = 650

or, x = \(\frac{650}{13}\)

\(\therefore\) x = 50

Hence, cost of the book = Rs 50

Solution:

Selling price of sari = Rs 1350

Profit (P) = Rs 150

Cost price of sari (CP) =?

We know that,

Profit = SP - CP

or, 150 = 1350 - CP

or, CP = 1350 -150

or, CP = 1200

∴ Cost Price (CP) of sari = Rs 1200

Solution:

Given,

Cost Price of the Calculator (CP) = Rs 760

Loss = Rs 50

Selling Price (SP) = ?

We know that,

Loss = CP - SP

or, 50 =Rs 760 - SP

or, SP = Rs 760 - Rs 50

or, SP = Rs 710

∴ Selling Price of the Calculator (SP) = Rs 710

Solution:

Given information,

Marked Price = Rs 450

Discount amount = 20% of RS 450

= \(\frac{20}{100}\)× 450

= Rs 90

Here

Selling Price = Marked price - Discount amount

= Rs 450 - Rs 90

= Rs 360

Solution:
Given information,

Marked Price = Rs 250

Selling Price (SP) = Rs 200

Discount = MP - SP

= Rs 250 - Rs 200

= RS 50

Here,

Discount Percentage = \(\frac{discount}{MP}\)× 100

= \(\frac{50}{250}\)× 100

= 20%

Solution:

Given information,

Selling Price = Rs 342

Let the marked price be x.

Then,

Discount amount = 10% of x

= \(\frac{10x}{100}\)

= \(\frac{x}{10}\)

Marked Price = SP + Discount amount

or, x = 342 + \(\frac{x}{10}\)

or, x - \(\frac{x}{10}\) = 342

or, \(\frac{10x -x}{10}\) = 342

or, 9x = 3420

\(\therefore\) x = \(\frac{3420}{9}\) 380

Hence, the marked price of the Article = Rs 380

Solution:

Given information,

Selling Price (SP) before VAT = Rs 4500

Selling Price (SP) after VAT = Rs 5000

VAT amount = SP with VAT - SP before VAT

= Rs 5400 - Rs 5000

= Rs 400

\(\therefore\) VAT rate = \(\frac{VAT amount }{SP before VAT}\)× 100

= \(\frac{400}{5000}\)× 100

= 8%

Solution:

Given information,

Marked Price = Rs 1,250

Discount Percent = 5%

Actual Price of watch = MP - Discount Percentage

= Rs 1,250 - Rs 1,250 × \(\frac{5}{100}\)

= Rs 1,250 - Rs 62.50

= Rs 1,187.50

∴ Actual Price of watch = Rs 1,187.50

Solution:

Given information,

Marked Price of Radio(MP) = Rs 1160

Selling Price after discount (SP) = Rs 1044

Now,

Discount = MP - SP

= Rs 1160 - Rs 1044

= Rs 116

∴ Discount Percentage = \(\frac{Discount Amount}{MP}\)× 100

= \(\frac{116}{1160}\) × 100

= 10%

Solution:

Given information,

Marked Price (MP) = Rs 210

Discount Percent = 12%

Discount amount = 12% of MP

= 210× \(\frac{12}{100}\)

= Rs 25.20

∴ Actual Price of the Book = Marked Price - Discount

= Rs 210 - Rs 25.20

= Rs 184.80

0%
  • Find the profit percent or loss percent in the given case:

    CP=Rs 400, Profit=Rs 80

    20%
    25%
    30%
    15%
  • Find the profit percent or loss percent in the given case:

     CP=Rs 275, loss=Rs 25

    10%
    12%
    9.09%
    15%
  • Find the profit percent or loss percent in the given case:

     SP=Rs 320, Gain=Rs 70

     

    15%
    20%
    28%
    25%
  • Find the profit percent or loss percent in the given case:

     SP=Rs 250, Loss =Rs 50

     

    14%
    15.67%
    16.25%
    16.67%
  • Find the profit percent or loss percent in the given case:

    CP = Rs 400, SP = Rs 475

    19.70%
    28.25%
    18.75%
    15.35%
  • A man purchased a bicycle for Rs 2000 and sold it for Rs 2400.Find his gain percent.

    25%
    20%
    10%
    30%
  • Sabina bought refrigerator for Rs 9900 and sold it for Rs 9000. Find her loss percent.

    5.25%
    8.85%
    9.095%
    8%
  • The cost price of 11 pens is equal to the selling price of 10 pens. find the gain or loss percent.

    8%
    5%
    12.25%
    10%
  • Renu bought a bicycle for Rs 5000 and sold it at a profit of 8%.Find her selling price.

    Rs 5300
    Rs 5500
    Rs 5400
    Rs 5000
  • Tripti bought a television for Rs 20000 and sold it at a loss of 12% find the selling price of the television.

    Rs 18600
    Rs 18600
    Rs 17650
    Rs 17600
  • Tripti bought a television for Rs 20000 and sold it at a loss of 12% find the selling price of the television.

    Rs 27600
    Rs 18600
    Rs 17500
    Rs 17600
  • By selling an article for Rs 864, a shopkeeper earns a profit of 8%, Find the  cost price.

    Rs 600
    Rs 500
    Rs 800
    Rs 650
  • A man sold the radio at the loss of 12 %. If the selling price was Rs 7040, what was its cost price?

     

    Rs 8400
    Rs 8000
    Rs 8500
    Rs 7000
  • Riya sold a bicycle at a loss of 20 %. If she sold it for Rs 800 more, she would have received a profit of 5%. Find the cost price.

    Rs 3300
    Rs 3250
    Rs 4200
    Rs 3200
  • Ujila sold her gold necklace at a profit of 7%. If she had sold it for Rs 294 more she would have got 10% profit. Find the cost price of the necklace.

     

     Rs 9800
     Rs 9700
     Rs 9895
     Rs 9810
  • A wholesaler marks the price of his goods 40% above the cost price and allows 20% discount. If his purchase price of an item is Rs, 1000, how much should a customer pay for it with 15% tax?

     

    Rs 1500
    Rs 1610
    Rs 2300
    Rs 1700
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Anoj

1. a man sells a tv for rupees 3450and makes a profit of 15% . he sells a second tv set at a loss of 10%.if on the whole he neither gains nor loses , find the cost price of the second tv.


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pratham

formula of C.P


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what is formulae of discount


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