### Profit and Loss- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems related to time and work. Basic knowledge regarding work done by given persons in specific time and related problems is important for various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

### Important Fact:

• If we buy a book for Rs. 100. It is called cost price (CP).
• If we sell it for Rs. 120. It is called selling price (SP) with profit of Rs. 20.
• If we sell it for Rs. 90, we will incur loss of Rs. 10.
• If we mark selling price as Rs. 120 but sell it for Rs.110 than Rs. 10 is called discount.

### Important Formulae:

• Profit / Gain = SP - CP
• Loss = CP - SP
• Gain % = (Gain x 100) / CP
• Loss % = (Loss x 100) / CP
• SP = {(100 + Gain%)/100} x CP
• CP = {100 / (100 + Gain%)} x SP
• SP = {(100 - Loss%)/100} x CP
• CP = {100 / (100 - Loss%)} x SP

Eg 1:  Mohan purchased an article for Rs. 520 and sold it for 650. Find the profit and percent of profit earned by Mohan?

Soln: CP = 520
SP = 650
Profit = SP - CP = 650 - 520 = 130
Profit % = (Profit x 100)/ CP = (130 x 100) / 520 = 25%.

Eg 2: Monika purchased an article for Rs. 1280 and sold it for 920. Find the loss incurred and loss percent?

Soln: CP = 1280
SP = 920
Loss = CP - SP = 1280 - 920 = 360
Loss% = (Loss x 100) / CP = (360 x 100) / 1280 = 28.125%

Eg 3: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

Soln: CP = 1400
Loss % = 15
SP = {(100 - Loss%)/100} x CP = {(100 - 15) 100} x 1400
SP = 1190.

Eg 4: When a plot is sold for Rs 18700, the owner loses 15 %. At what price must the plot be sold in order to gain 15 %?

Soln: SP = 18700
Loss % = 15
CP = {100 / (100 - Loss%)} x SP = {100 / (100 - 15)} x 18700 = 22000

Now to gain 15 % gain we need to find new SP

SP = {(100 + Gain%)/100} x CP = {(100 + 15) / 100} x 22000 = 25300.

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