Profit & Loss Shortcut Methods:
- Gain% or Loss % = [(Loss or Gain)/cp ]*100
- Selling Price = [(100+g%)/100]Cost Price or [(100-L%)/100]*100.
- Gain% = [Error/(True Value-Error )]*100
- Sold Goods with 960 gms instead of kg.
Gain% = (40/960)*100.
- Purchases 11 oranges for 10 Rs/-.10 oranges for 11 Rs/-.
Profit or Loss = [(11*11) – (10*10)]/(10*10).
- 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.
- The salesman sells goods at x% loss but uses y gms instead of z gms. Find Gain or Loss?
- Dealer sells goods at x% loss but uses y% less weight. Find profit or loss?
[[(100-x) / (100-y)]*100 – 100].
- Seller uses x gms in place of 1000 gms and bears y% loss.
Actual Gain or Loss = (100-y)[1000/x] – 100.
- 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%).
- 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.
- Cost price of x articles is equal to
Selling price of y articles. Then profit% = [(x-y)/y]%.
- By selling 66 metres cloth a person gains cost of 22 metres. Then, Gain%= [22/66 ]*100.
- The market price of goods at x% above the cost price discount allowed y%.
Then, Profit or Loss% = x-y-xy/100.
- 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.
- Selling price = [market price(100-discount%)]/100.
- Selling price = market price – discount.
- Discount% = (discount/market price)*100.
- Market Price= [(100+P%)/(100-D%)]*Cost Price.
- 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).
- 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,
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=?
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)
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
- [(100+25)/100] CP
Or use this formula P% or L% = [(CP-SP)/SP]*100 i.e. [(20 -16)/16]*100 =1/4 (100)% i.e. 25%