**Profit & Loss**

If you understand concept of profit and loss you don’t need any shortcut Formulas to solve it. For understanding profit & loss you need to understand main four concept

(1) Cost Price (C.P)

(2) Selling Price (S.P)

(3) Profit & (4) Loss.

Lets see this terms means.

Consider a scenario, where you are a shop keeper and you want to selling Soap, so for the sell something you need to have something, so you go to a whole sell dealer and you buy a soap.

Example you buy it for 5 Rs. This 5 Rs you had paid so this becomes your cost prise is 5 Rs.

CP = 5 Rs.

Now your friends need to barrow a soap, so you sell it to him for 6 Rs. so SP = 6 Rs.

You purchased it for 5 R.s and Sold it for 6 Rs. So you will get a profit of 1 Rs, that is your profit.

If your cost price(C.P) = 5 and Selling Price( S.P) = 4, So you have an Loss of 1 Rs.

So if you understand this, basically the Profit and Loss is totally is depend on Selling Price and Cost Price. So the selling price is more then you will have an profit and if the selling price is less than your cost price then you have an Loss.

(1) Cost price (CP) is the price at which an article is purchased.

(2) Selling price (SP) is the price at which an article is sold.

(3) If SP > CP, it is a profit or gain

(4) If CP > SP, it is a loss.

(5) Gain or Profit = SP – CP

(6) Loss = CP - SP.

Just consider this, you have an 100 bath of Soap and you sold 10, and suppose compotation is increased and you have to low your prices, and next 10 at some different prices. if you calculated on the selling price you will never get a right answer, Your Cost Price is always Fixed. If you observed in both the scenario 5 Rs. Is always fix your selling price is changes. So the loss and profit both are Calculated on Cost Price

**Important Formulas - Profit and Loss**

**(7) Loss or gain is always Depend on CP**

(8) Profit Percentage (Profit %) = Profit / C.P ×100 = (S.P-C.P) / C.P × 100

(9) Loss Percentage (Loss %) = Loss/C.P × 100 = (C.P-S.P) / C.P × 100

(10) In the case of a gain or profit,

S.P = (100 + Gain%)/100 * C.P

C.P = 100 / (100 + Gain%)*S.P

(11) In the case of a loss,

S.P = (100 - Gain%) / 100 * C.P

C.P = 100 / (100 - Gain%)* S.P

(12) If an article is sold at a gain of 20%, then SP = 120% of CP.

(13) If an article is sold at a loss of 20% then SP = 80% of CP.

(14) If an article is sold at a loss of 20% then SP = 80% of CP

(15) If a person sells two items at the same price; one at a gain of x % and another at a loss of x %, then the seller always incurs a loss expressed as

Loss% = (Common Loss & Gain %)^2 / 10 = C.P. = (X/10)^2

(16) If a trader professes to sell his goods at cost price, but uses false weights, then

Gain% = Error/(True Value - Error) * 100

(16) Discount(Discount %) = (M.P - C.P)/M.P *100

(17) Mark Up(Mark Up %) = (M.P-C.P)/C.P * 100

**Problem 1**: The Ratio of the cost price to the selling price is 4:5. Find the profit percentage .

**Solution**: They given the Ratio of Cost Price : Selling Price = 4 : 5

Generally if selling Price is more than Cost Price then you have an Profit.

Gain = S.P – C.P = 5 – 4 = 1

Gain Percentage will be calculated upon CP

Gain % = 1/C.P *100% = 1/4*100 = 0.25 ×100 = 25%.

**Problem 2**: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:

**Solution**: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.

Selling Price (S.P.) = Rs. 5800.

Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.

Gain% = 300/500*100 = 5* 5/1 %

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