Profit and Loss

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Cost Price (CP) 

The buying price of any item is known as its cost price.It is written in short as CP.

Selling Price (SP) 

The price at which any item is sold is known as the selling price.It is written in short as SP.

Profit or Gain 

Financial benefit realised after selling an item is called profit or gain.
For any item, when SP is more than CP, then we say that profit occurred on selling that item.

Loss 

Financial drawback realised after selling an item is called loss.
For any item, when CP is more than SP, then we say that loss occurred on selling that item.

• CP < SP    ⇒ Profit = SP – CP
• CP = SP    ⇒ No profit no Loss
• CP > SP    ⇒ Loss = CP – SP  

(Q) How would we interpret these statements related to prices of items.
1) A toy bought for Rs 72 is sold at Rs 80.
2) A T-shirt bought for Rs 120 is sold at Rs 100.
3) A cycle bought for Rs 800 is sold for Rs 940.
(A) We can interpret the above statements as following -
  1) CP of the toy = Rs 72 
      SP of the toy = Rs 80.   
      ∵ SP > CP
      ⇒ Profit = SP − CP = Rs 80 − Rs 72 = Rs 8
  2) CP of the shirt = Rs 120
      SP of the shirt = Rs 100.   
      ∵ SP < CP
      ⇒ Loss = CP − SP = Rs 120 − Rs 100 = Rs 20
  3) CP of the cycle = Rs 800
      SP of the cycle = Rs 940.   
      ∵ SP > CP
      ⇒ Profit = SP − CP = Rs 940 − Rs 800 = Rs 140.

Profit or Loss as a Percentage

➣ In Percentage we have learned about increase percent and decrease percent, we can apply that to get profit percent and loss percent.
➣ In case of profit there is increase in price .e., the profit, where CP can be treated as base or original amount.
➣In case of loss there is decrease in price .e., the loss, where CP can be treated as base or original amount.

➣ Profit % = ^PROFIT/ _CP × 100
     Profit % = ^(SP−CP)/ _CP × 100
➣ Loss % = ^LOSS/ _CP × 100
     Loss % = ^(CP−SP)/ _CP × 100

Try These

1. A shopkeeper bought a chair for Rs 375 and sold it for Rs 400. Find the gain Percentage.
2. Cost of an item is Rs 50. It was sold with a profit of 12%. Find the selling price.
3. An article was sold for Rs 250 with a profit of 5%. What was its cost price?
4. An item was sold for Rs 540 at a loss of 5%. What was its cost price?

Solution

1). Gain = Rs (400-375) = Rs 25
   ∴ Gain % = ^Gain/ _CP ×100 = ²⁵/ ₃₇₅ ×100
                   = ¹/ ₁₅×100 = ¹/₃×20 = 6²/₃%

2). Let SP be Rs x, then
     Gain % = ^{(SP- CP)}/ _CP ×100
     ⇒ 12 = ^(x-50)/ ₅₀ ×100
     ⇒ 12 = ^(x-50)/ ₁ ×2 =  2(x-50)
     ⇒ 2(x-50) = 12         (rearranging)
     ⇒ x-50 = ¹²/₂ =6
     ⇒ x = 6+50 = 56
    ∴ SP of the item = Rs 56

3). Let CP be Rs x, then
     Gain % = ^{(250- x)}/ _x ×100
     ⇒ 5 = ^(250- x)/ _x  ×100
     ⇒ 5x = 100(250-x)
     ⇒ x = ^{100(250- x)}/ ₅     
     ⇒ x = 20(250-x) = 5000 - 20x
     ⇒ x + 20x = 5000
     ⇒ 21x = 5000
     ⇒ x = ⁵⁰⁰⁰/ ₂₁ = 238.09
    ∴ CP of the item = Rs 238.09

4). Let CP be Rs x, then
     Loss % = ^(x -540)/ _x ×100
     ⇒ 5 = ^(x -540)/ _x ×100  
     ⇒ 5x = 100(x-540)
     ⇒ x = ^100(x-540)/ ₅     
     ⇒ x = 20(x-540) = 20x - 20×540
     ⇒ 20×540 = 20x − x
     ⇒ 19x =  20×540             (rearranging)
     ⇒ x = ^20×540/ ₁₉
     ⇒ x = 560⁸/₁₉
    ∴ CP of the item = Rs 560.42

Overhead Expenses

➢ Sometimes when an article is bought, some additional expenses are made while buying or before selling it. These expenses are sometimes referred to as overhead charges.
➢ It may include expenses like amount spent on repairs, labour charges, transportation etc.
➢ Overhead expenses have to be included in the cost price.
   ∴ CP = Buying price + Overhead charges
Q). Find selling price (SP) if a profit of 5% is made on
(a) a cycle of Rs 700 with Rs 50 as overhead charges.
(b) a lawn mower bought at Rs 1150 with Rs 50 as transportation charges.
(c) a fan bought for Rs 560 and expenses of Rs 40 made on its repairs.

A). Profit = 5%
(a) CP = Rs 700 + Rs 50 = Rs 750
     Let SP be x
      Profit % = ^{(SP- CP)}/ _CP ×100
     ⇒ 5 = ^(x-750)/ ₇₅₀ ×100
     ⇒ 5×75 = 10(x-750)
     ⇒10(x-750) = 5×75         (rearranging)
     ⇒ x-750 = ^5×75/₁₀ = 37.5
     ⇒ x = 37.5+750 = 787.5
    ∴ SP of the item = Rs 787.5

(b) CP = Rs 1150 + Rs 50 = Rs 1200
     Let SP be x
      Profit % = ^{(SP- CP)}/ _CP ×100
     ⇒ 5 = ^(x-1200)/ ₁₂₀₀ ×100
     ⇒ 5×12 = (x-1200)
     ⇒ x-1200 = 5×12         (rearranging)
     ⇒ x-1200 = 60
     ⇒ x = 60 + 1200 = 1260
    ∴ SP of the item = Rs 1260

(b) CP = Rs 560 + Rs 40 = Rs 600
     Let SP be x
      Profit % = ^{(SP- CP)}/ _CP ×100
     ⇒ 5 = ^(x-600)/ ₆₀₀ ×100
     ⇒ 5×6 = (x-600)
     ⇒ x-600 = 5×6         (rearranging)
     ⇒ x-600 = 30
     ⇒ x = 30 + 600 = 630
    ∴ SP of the item = Rs 630

Percentage
	Discount & Taxes ➤