If CP is the Cost Price and SP is the Selling Price then profit and loss can be calculated using the below formulas:

**Profit:**

When SP is greater than CP it means profit occurs.

Profit=SP-CP

Profit %= (Profit/CP)*100 %

**Loss:**

When CP is greater than SP it means loss occurs.

Loss=CP-SP

Loss %=(Loss/CP)*100%

**Note: **Loss and Gain is always checked on CP.

**SP Calculation Formula:**

**If Gain Occur:**

**If Loss Occur:**

**CP Calculation Formula:**

**If Gain Occur:**

**If Loss Occur:**

**Note:**

- If two similar articles are sold, one at a gain of a% and other at a loss of a% then always loss is occurred and loss percent is:

Loss Percent= a*a/100 %

- If a trader sell his items at CP but uses false weight, then

**Trick**

If a person sells his one article at X % loss and other at X% profit then there will be loss only

And calculated as under:

**Loss %= (X/10) ^{2}**

**Trick**

If a shopkeeper sell his articles at loss or profit % (x) and also measure less than actual measure then gain or profit (g) will be calculated by below formula

**(100+g)/(100+x)=True measure /False measure**

**Exercises**

**1.A shopkeeper bu 40 kg wheat at Rs 15 per kg and sells it in Rs 20 per kg.What is profit and profit percentage?**

Answer:

Here, cost price CP of 40kg wheat=40*15 =Rs 600

Selling Price SP =40*20=Rs 800

Therefore,

Profit =SP-CP=800-600=**Rs. 200**

Profit Percent % =(Profit/CP)*100

=(200/600)*100

**=33.33%**

**2.If Cost price of 30 books is equal to Selling price of 20 books then what is profit or loss percent?**

Answer:

Let, CP of 1 book = RS. 1

Then CP of 30 Books = Rs 30

According to question,

SP of 20 Books = Rs 30,

SP of 1 Book= 30/20,

SP of 30 Books =30*30/20

=Rs 45

Therefore, Profit = SP-CP

=45-30

=Rs. 15

Profit Percent = (15/30)*100

**=50%**

**3.If a Shopkeeper sells all his goods at 10 % profit and he weigh 100 Gram less per kg then what is profit percent?**

**Answer:**

**Trick**

**(100+g)/(100+x)=True measure /False measure**

Where g=loss/ profit %

x =profit or loss at CP

Therefore,

(100+g)/(100+10)=1000/900

- (100+g)=10*110/9
- g=(1100-900)/9
- g=200/9 %
**Hence, Profit percent = g=200/9 %**

**4.A person buy 4 kg more Sugar in Rs. 320 if price of sugar is reduced by 15% then what is reduced price of sugar per kg?**

**Answer:**

**Reduced price of sugar /kg = % reduction in price*Price/Quantity**

=(15/100)*320/4

**=Rs 12**

**5.A shopkeeper buys two fans in Rs 2000 and he sells one @ 20 % profit and second @ 25% loss. If selling price of each fan is same then what is Cost price of each fan.**

**Answer:**

Let, CP of one Fan= Rs X

And CP of Second= Rs.( 2000-X)

SP_{1} of one fan= X*(100+20)/100 =120*X/100

SP_{2} of Second fan =(2000-X)*(100-25)/100

According to question,

SP_{1=} SP_{2}

- 120*X/100= (2000-X)*(100-25)/100
- 120X=75*(2000-X)
- 120X=75*2000-75X
- 195X=150000
- X=Rs. 770

Therefore,

**SP _{1}=Rs. 770 and SP_{2}=(2000-770)=Rs. 1230**

**6.A man decided to sells his two Mobile phone at Rs 5000 each and one at 10 % profit , other at 10% loss. Find out the loss percent .**

Answer:

**Trick**

**If a person sells his one article at X % loss and other at X% profit then there will be loss only **

**And calculated as under:**

**Loss %= (X/10) ^{2}**

Hence, Loss % = (10/10)^{2}

**=1%**

** **