# 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 = Aptitude Profit & Loss Test Paper 1
Aptitude Profit & Loss Test Paper 2
Aptitude Profit & Loss Test Paper 3
Aptitude Profit & Loss Test Paper 4
Aptitude Profit & Loss Test Paper 5

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