Profit  & Loss  Shortcut Methods:

1. Gain% or Loss % = [(Loss or Gain)/cp ]*100
2. Selling Price = [(100+g%)/100]Cost Price or [(100-L%)/100]*100.
3. Gain% = [Error/(True Value-Error )]*100
4. Sold Goods with 960 gms instead of kg.

Gain% = (40/960)*100.

5. Purchases 11 oranges for 10 Rs/-.10 oranges for 11 Rs/-.

Profit or Loss = [(11*11) – (10*10)]/(10*10).

6. Grocer sells rice at a profit of 10% and uses weight 20% less .Find total gain%?

Gain% = [(P%) + Less in weight%]/100-less in weight% * 100.

7. The salesman sells goods at x% loss but uses y gms instead of z gms. Find Gain or Loss?

[(100-x)z/y]-100.

8. Dealer sells goods at x% loss but uses y% less weight. Find profit or loss?

[[(100-x) / (100-y)]*100 – 100].

9. Seller uses x gms in place of 1000 gms and bears y% loss.

Actual Gain or Loss = (100-y)[1000/x] – 100.

10. A sells goods to B at x% profit and B sells it to C at y% profit. If C pays 225.Then what is cost price of A?

Sol:  P% = x+y +xy/100.

        Cost price of A = 225 * 100/(100+P%).

11. Book sold at 12% profit. If it is sold 18 Rs/. More, we get 18% more profit. Find Cost price?

Sol: Cost price = (More Gain/ Diff in profits) *100.

12. Cost price of x articles is equal to

Selling price of y articles. Then profit% = [(x-y)/y]%.

13. By selling 66 metres cloth a person gains cost of 22 metres. Then, Gain%= [22/66 ]*100.
14. The market price of goods at x% above the cost price discount allowed y%.

Then, Profit or Loss% = x-y-xy/100.

15. By selling an article at 1380. If is 15% gained. Find selling priced to gain 25%.

Sol: 115% à 1380.

125% à ?

i.e. selling price= (125*138) /115.

= 150.

16. Selling price = [market price(100-discount%)]/100.
17. Selling price = market price – discount.
18. Discount% = (discount/market price)*100.
19. Market Price= [(100+P%)/(100-D%)]*Cost Price.
20. If A sells to B at profit of R1%, B sells to C at a profit of R2%,

C sells to D at a profit of  R3%. Then,
Cost Price of D = Cost price of A(1+R/100)(1+R2/100)(1+R3/100).

21. A dealer purchases some articles at X Rs. And some articles at Y Rs. Then mixes and sells at Z Rs/-. Then

Gain or loss = [(2xy/z(x+y))-1]*100.

Profit and Loss Practice Questions with Solutions:

Problem 1: If cost price of two articles C1 & C2 are same and also P% of one article is equal to loss% of another . then there will be no loss no gain.

Sol: (cost price) C₁= C₂ , P₁ % = L₂% So there is no loss no gain.

Note : If selling price (SP)₁  = (SP)₂  and P₁ % = L₂%.

Then The overall loss or profit% is (x²/100)%.

Problem 2:  An article is sold at a loss of 10%. If the SP is increased by 45 Rs. Then the profit made would be 5%. Find Cp of the article.

Sol: When Loss = L% ,  Then SP(selling price) = (100 – L)% of CP(cost price).

Here, (SP)₁ = (100- 10)% of CP

= 90% of CP.

When Profit = P%, Then SP =(100+P)% of CP.

Here, (SP)₂ = (100+5) % of CP.

= 105% CP.

SP₁ – SP₂ = 45

15% of CP =45

CP = 45 *100/15 = 300 Rs.

Problem 3:  Praveen sold an article for 1170 Rs. At a profit of 30%. What should be the SP If desired profit is 40%?

Sol:  Here,  Old SP = 130% of CP à 1170

New SP = 140% of CP à      ?

With cross multiplication,

• (1170*140)/130
• 1260.

Problem 4:   The profit earned by selling a phone for 18000 Rs. Is same as the loss incurred by selling for 16800 Rs.What is the cost price?

Sol:  SP –CP = CP¹ – SP¹

• 2CP = SP + SP¹
• CP = 17400.

Problem 5: A watch was sold at the loss of 9%. It was observed that  If the selling price was 420 Rs. More profit made was 5 %. What was the original selling price?

Sol: L%= 9% Then SP₁ = 91% of CP

P% = 5 % Then SP₂ = 105% of CP

Here 14% of CP = 420,

• 91% of CP=?
• (91*420)/14

Problem 4:   A shopkeeper marks his goods in such a way that even after allowing the discount of 20%  he makes the profit of 12%. How much % above the cost price is the marked price?

Sol: CP =100(assume)

P% =12%

SP= 112% of 100 = 112

Discount = 20%

SP = (100-20) % of MP(marked price)= 80% of mp

• sp = 112

mp=(100*112)/80 = 140.

Problem 4:   Sridhar sold 16 pens at the cost of 20 pens. What is the profit or loss% made by him?

Sol: 16 SP = 20 CP

SP = 5/4 CP

• (125/100)CP
• [(100+25)/100] CP

SP= 25%

Or use this formula P% or L% = [(CP-SP)/SP]*100       i.e.    [(20 -16)/16]*100 =1/4 (100)% i.e. 25%