In this article, we will find a way to solve these question within a matter of time.

Basic Concepts of Profit And Loss

First, let’s look at basic concepts:

Cost price: The price you require to pay to purchase a product

Market Price: The price you see on a product

MP= SP + D

Selling price: The price on which you sell a product

SP = CP + P OR CP – L

Discount: This is imposed on Market price and deducting it from MP to get selling price

D = MP – SP

Profit: When the cost price is lesser than the selling price

P = SP – CP

Loss: When the cost price is higher than the selling price

L= CP-SP

Net Profit or Loss in %= L/CP *100 or P/CP * 100

Types of Questions Asked From Profit and Loss Problems

• When selling price and % profit or % loss are given in the question, and we need to find CP

  • If %profit is given then, (100/100+%profit)* SP
  • If %loss is given then, (100/100-%loss)*SP

Q. A product was sold for Rs. 200 on 20% profit. What will be the cost price of the product?

Since it is a profit,

=(100/120)*200

=Rs 166.6

• When Cost price and % profit or % loss are given in the question, and we need to calculate SP

  • If %profit is given then, (100+%profit/100)* CP
  • If %loss is given then, (100-%loss/100)*CP

Q. A product was purchased for Rs. 200 and sold on 20% profit. What will be the cost price of the product?

Since it is profit,

=((100+20)/100)*CP

=(120/100)*200

=Rs 240

• When a product’s SP and %profit or %loss are given and we have to find at what cost it should be sold to achieve given %profit or %loss

  • SP * (100+ %profit to achieve[ – if loss to achieve]/100-%loss [+ %profit]

Q. A product was sold for Rs. 200 on 20% profit. At what cost it should be sold to have 40% profit?

= 200*((100+40)/(100+20)

=200*(140/120)

= 200*(7/6)

= Rs. 233.3

• When SP of a product is given and %profit or %loss is same as cost price. Find cost price

  • In the case of profit, find two number whose multiplication give SP(LCM of SP will give you two combinations) and whose subtraction give give 10.
  • In the case of loss, find two number whose multiplication give SP(LCM of SP will give you two combinations) and whose addition give 10.
  • And put 0 at one’s place of a smaller number

Q. A product was sold for Rs. 75 with the same amount of %profit as cost price. What is the cost price?

Find two number whose multiplication and subtractions are 75 and 10

They are 15 and 5

So, 15*5 =75 and 15-5 =10 , condition satisfied

put 0 in front of smaller number which is 5

Rs. 50 is the answer

• When Selling price of a product with %profit or %loss are given. We need to find same product’s SP if it intends to be sold on %profit or %loss

  • In Such case, SP/ quantity*(100+ %profit [- if %loss]) = SP/ quantity*(100+ %profit [- if %loss])

Q. Products were sold for Rs. 200 with a profit of 20%. At what cost it should be sold to have 40% profit

200/(20*120) = x/(20*140)

(200/2400) = x/2800

(1/12) = x/2800

2800=12x

= Rs. 233.3

• When two products sold at the same price each. The first product made %profit and other incurred %loss, then Find net %profit or %loss

  • Make tables for each product having three columns CP, P/L and SP
  • Find the %profit or %loss in form of its respective fraction and place it in the table, i.e 20% profit , 1/5, CP = 5, p =1, SP= 6
  • Balance the selling price and by multiplying both side
  • find a net difference between Profit and loss
  • And add the CP
  • And find the % of the increase

Q. A man bought two bicycles for Rs. 750 each. If he sells one at a profit of 10%, and others at a loss of 10%, find net profit or loss in %?

So , Fraction of profit 10% = 10/100 = 1/10 = CP 10, P 1, SP 10+1 , 11

Fraction of loss 10% = 10/100 = 1/10 = CP 10, L -1, SP 10-1 , 9

(-2/189)*100

Loss of 0.01%