## PROFIT & LOSS

1. Profit = Selling Price - Cost price

2. Selling Price = Cost Price + Profit

3. Cost Price = Selling Price - Profit

4. Loss = Cost Price - Selling Price

5. Selling Price = Cost Price - Loss

6. Cost price = Selling Price + Loss
Gain% = (Gain/C.P)*100
Loss% = (Loss/C.P)*100
7. Percentage profit / loss is always calculated on CP unless otherwise stated.

8. Profit Percentage = (Profit x 100) / CP

9. Loss Percentage = (Loss x CP) / CP

10. Selling Price = {[(100+ Gain %) x CP] / 100}

11. Selling Price = {[100- Loss %) x CP] /100}

12. Cost Price = {(100 x SP) / (100+ Gain %)}

13. Cost Price = {(100 x SP) / (100 - Loss %)}

14. If a man buys 'p' articles for 'a' rupees and sells 'q' articles for 'b' rupees. Then,
The % profit or loss = (p x b) - (q x a) / (a x q).
Note: If the Sign is +ve, there is gain. If the sign is -ve, there is a loss.
Eg : A trader buys oranges at 9 for Rs. 16 and sells them at 11 for Rs. 20. What does he gain or lose percent?

Ans: % profit or loss = [(9 x 20) - (16 x 11)]/ 16 x 11
= 2 3/11 %.
Since the sign is +ve, there is a gain of 2 3/11%.

15. If a shopkeeper sells his goods at x% loss on cost price but uses y gm instead of z gm, then,

His % profit or loss = [(100 - x) (z/y)] - 100.

Eg: A dishonest trader sells goods at 6 ¼ % loss on cost price but uses 875 gm instead of 1 kg. What is his percentage profit or loss?

Ans: Profit or loss percentage = [(100-6 ¼) (1000/875)] - 100
= [(375/4) (8/7)] - 100
=(107.1428) -100
= 7.1428 %
Since sign is +ve, there is a profit of 7.1428%.

16. If a shopkeeper sells his goods at x% profit on cost price but uses y gm instead of z gm, then,

His % profit or loss = [(100 + x) (z/y)] - 100.

Eg: A dishonest trader sells goods at 4 % gain on cost price but uses 840 gm instead of 1 kg. What is his percentage profit or loss?

Ans: Profit or loss percentage = [(100+4) (1000/840)] - 100
= [123.8095] - 100
= 23.8095%
Since sign is +ve, there is a profit of 7.1428%.

17. When two articles are sold at the same price such that there is a Profit of x % on one article and a Loss of x% on the other. Then Percentage Loss is:
= (Common profit or loss) 2 /100
= X2 /100

18. Marked Price or List Price is the price that is indicated or marked on the product or it is the price, which is given in the price list. This is the price at which the product is intended to be sold. However, there can be some DISCOUNT given on this price and consequently, the actual Selling Price of the product may be less than the Marked Price.
Selling Price = Marked Price - Discount.

19. Discount Percent = (Marked Price - Selling Price) x 100 / Marked Price

20. If the successive discounts given on a product are p%, q% and r%, then the selling price after all the discounts is:

= [Marked Price x (100-p) (100-q) (100-r)]/ 100 x 100 x 100
21. If 'x' articles are purchased for 'p' rupees and 'y' articles are sold for 'p' rupees. Then, Percentage profit / loss = (x-y) / y.

22. If selling price of 'x' pens is equal to the cost price of 'y' pens. Then profit percentage = (y-x) x 100 / x

E.g 2: The selling price of 12 pens is equal to the cost price of 20 pens. Find the profit percentage?

Ans: Percentage profit = (20 - 12) / 20
= 8/20
= 66.66%.
E.g3: If 12 oranges are purchased for Rs. 100 and 10 oranges are sold for Rs. 100. Find the percentage profit / loss ?

Ans: Percentage Profit = [(12 - 10) /10]x 100.
= (2 /10) x 100
= 20 %.

23. By using false weight, if a substance is sold at cost price the overall gain % is given by [(100 + Gain %) / 100]. = True weight/ False weight.

24. By selling an article for Rs. X, a man loses l%. At what price should he sell it to gain y%? (or)

A man lost l% by selling an article for Rs. X. What percent shall he gain or lose by selling it for Rs. Y?

(100 – loss%) : 1st S.P. = (100 + gain%) : 2nd S.P.

25. A man sold two articles for Rs. X each. On one he gains y% while on the other he loses y%. How much does he gain or lose in the whole transaction?

In such a question, there is always a lose. The selling price is immaterial.

Formula for loss % 