Before starting with profit and loss lets take up some statements related to percentages which I have not discussed before and which are helpful in solving questions involving concept of percentages including questions of profit and loss, partnerships, stocks and shares. These formulas are also helpful while dealing with Simple Interest and Compound Interest.

**If the value of an item goes up by r %, the percentage reduction that should be made to bring it back to the initial/original value = ((100r)/(100+r)) %**

*Statement 1.***If the value of an item goes down by r %, the percentage increase that should be made to bring it back to the initial/original value = ((100r)/(100-r)) %**

*Statement 2.***If X is r % more than Y, then Y is ((100r)/(100+r)) % less than X.**

*Statement 3.***If X is r % less than Y, then Y is ((100r)/(100-r)) % more than Y.**

*Statement 4.***If the ticket cost of a movie increases by r % then the number of tickets sold should be reduced by ((100r)/(100+r)) % so that the collection remains same.**

*Statement 5.***If the ticket cost of a movie decreases by r % then the number of tickets sold should be increased by ((100r)/(100-r)) % so that the collection remains same.**

*Statement 6.**Basic Terms that we often see while dealing with questions of Profit and Loss -*

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**- It is that price of an article on which it is sold.***SELLING PRICE(SP)*
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**- It is that price of an article on which it is purchased.***COST PRICE(CP)*
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**- If the SP of an article is greater than its CP then there will be profit for that article equal to (SP - CP)***PROFIT/GAIN*
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**- If the CP of an article is greater than its SP then there will be loss for that article equal to (CP - SP)***LOSS*
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**= (SP - CP)100/CP = (Profit)100/CP***PERCENTAGE PROFIT(P %)*
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**= (CP - SP)100/CP = (Loss)100/CP***PERCENTAGE LOSS(L %)*
Some other formulas -

1. SP = (CP)(100+P)/100 in case of profit

2. SP = (CP)(100-L)/100 in case of loss

3. CP = (SP)(100)/(100+P) in case of profit

4. CP = (SP)(100)/(100-L) in case of loss

*#An Article sold at two different selling price say SP1 and SP2 and cost price be CP. The gain percentage in both cases being P1 and P2, then the formula formed in this type of situation would be -*
CP/100 = SP1/(100+P1) = SP2/(100+P2)

Kindly note value of percentage will become negative in case of loss percentage.

**By selling an article for Rs. 450, a man loses 25 %. At what price should he sell in order to gain 50 %.**

*Question 1.*

*#When two different Articles are sold at same selling price*
In this we will discuss those cases where on one article we will be getting profit and on other we will be getting loss.

*1st case - Where profit percentage(p) and loss percentage(l) are not equal.*

Overall gain or loss percentage would be ((2(100+p)(100+l))/((100+p)+(100+l))) - 100

**A man sold two almirahs for Rs. 4800 each. One one, he gains 30 % and on other, he loses 20 %. How much does he gain or lose in the whole transaction ?**

*Question 2.**2nd case - Where profit percentage(r) and loss percentage(r) are not equal.*

In this type of cases overall only loss would be there.

Loss Percentage would be = -(r

^{2}/100)**Two watches were sold for Rs. 2000 each. One one, a gain of 20 % is made and on the other, a loss of 20 %. How much percentage loss or percentage gain is made in the whole transaction ??**

*Question 3.*
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