**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?

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

- 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.

= 150.

- 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) C_{1}= C_{2} , P_{1} % = L_{2}% So there is no loss no gain.

**Note : **If selling price (SP)_{1 } = (SP)_{2 } and P_{1 }% = L_{2}%.

Then The overall loss or profit% is (x^{2}/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.

SP_{1 }– SP_{2} = 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 = CP^{1} – SP^{1}

- 2CP = SP + SP
^{1} - 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 SP_{1 }= 91% of CP

P% = 5 % Then SP_{2} = 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%