# Profit & Loss

# Profit & Loss Concepts and Formulas

## Points to remember:

1) **Cost Price:** It is the price at which a product is purchased. It is commonly abbreviated as C.P.

2) **Selling Price:** It is the price at which a product is sold. It is commonly abbreviated as S.P.

3) **Profit or gain:** If the selling price of a product is more than the cost price, there will be profit in the deal.

Therefore, Profit or Gain = S.P. – C.P.

4) **Loss:** If the selling price of a product is less than the cost price, the seller will incur a loss.

Therefore, Loss = C.P. – S.P.

5) Profit or Gain % =__S.P.- C.P__ ∗100→__Profit__ ∗100

C.P C.P

6) Loss % =__C.P.- S.P__ ∗100→__Loss__ ∗100

C.P C.P

7) If there is a profit or gain in the deal or transaction;

Selling Price (S.P.) =__(100 + Profit %)__ ∗100

100

And, the Cost Price (C.P.) =∗S.P.

8) If there is a loss in the deal or transaction;

Selling Price (S.P.) =__(100 – Loss %)__ ∗C.P.

100

And, the Cost Price (C.P.) =∗S.P.

9) If an article is sold at a profit of X%, the selling price would be equal to X% of cost price .

10) If an article is sold at a loss of X%, the selling price would be equal to (100-X)% of cost price (__100 – X__ ∗C.P).

100

11) When a seller sells two similar items one at X% gain and another one at same (X %) loss, the seller always incurs a loss in the deal which is given by:

Loss %=(__Loss % ∗ Gain %__) %

100

### Some quicker methods to solve the problems:

1) If a seller claims that he is selling goods at cost price but uses false weight to earn profit;

% Profit =__(True Weight- False Weight)__ ∗100

False Weight

Or,% Profit =∗100

2) If a seller sells a product at X% loss but uses weight Y instead of Z, the % Gain earned or % loss incurred is given by:

= (100 – X)__Z__-100

Y

+ve sign will indicate profit and -ve sign will indicate loss.

3) If a shopkeeper uses weight Y gm instead of 1 kg and incurs an X% loss on cost price, his actual gain or loss % is given by:

= (100 – X)__100__-100

Y

+ve sign will indicate profit and -ve sign will show the loss.

4) If a shopkeeper uses weight Y gm instead of 1 kg and earns a profit of X% on cost price, his actual gain or loss % is given by:

= (100 + X)__100__-100

Y

+ve sign will indicate profit and -ve sign will indicate the loss.

5) If there are two successive profits of X% and Y% in a transaction, the resultant profit is given by:

Resultant profit = (X + Y +__XY__)

100

6) If there is a profit of X% and loss of Y% in a transaction, the resultant profit or loss is given by:

Resultant profit or loss = X Y –__XY__)

100

+ve sign will indicate profit and -ve sign will indicate the loss.

7) A seller sells a product at profit of X%. If he sells it for Rs. Z more, his profit would be Y%. In this case the Cost Price is given by:

C.P. =

8) If the cost price and selling price of a product are reduced by same amount (X), the cost price is given by:

C.P. =__(Initial profit % +Increase in profit %) ∗ X__)

Increase in profit %

9) If the cost price of P articles is equal to the selling price of Q articles, then profit % or loss % is given by:

10) If A sells a product to B at a gain or loss of P% and B sells it to C at a gain or loss of Q%, the final gain or loss is given by:

(P+Q+__PQ__)

100

+ve sign will indicate profit and -ve sign will indicate the loss.

11) If a shopkeeper marks the products at P% above the cost price and gives the customer a discount of Q%, the final profit or loss % is given by =

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