Profit and Loss

Profit and Loss
Image Credit: Pixabay.com

Peofit and Loss is the topic of quantitive math in which we compare the prices of an article (or articles) before and after the trade of that article (or articles).

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.

\boxed{Profit = SP - CP}

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.

\boxed{Loss = CP - SP}

  • 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.

\boxed{Profit \% = \frac{PROFIT}{CP}\times 100}

\boxed{Profit \% = \frac{(SP-CP)}{CP}\times 100}

\boxed{Loss \% = \frac{LOSS}{CP} \times 100}

\boxed{Loss \% = \frac{(CP-SP)}{CP}\times 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 % = \frac{Gain}{CP}\times 100 = \frac{25}{375}\times 100

= \frac{1}{15}\times 100 = \frac{1}{3}\times 20 = 6\frac{2}{3}\%

2). Let SP be Rs x, then,

Gain % = \frac{(SP-CP)}{CP}\times 100

\implies 12 = \frac{(x-50)}{50}\times 100

\implies 12 = \frac {(x-50)}{1}\times 2 = 2(x-50)

\implies 2(x-50) = 12\, (rearranging)

\implies x-50 = \frac{12}{2} =6

\implies x = 6+50 = 56

∴ SP of the item = Rs 56

3). Let CP be Rs x, then,

Gain % = \frac{(250-x)}{x}\times 100

\implies 5 = \frac{(250-x)}{x}\times 100

\implies 5x = (250-x)100

\implies x = 100(250-x)\frac{100}{5}

\implies x = (250-x)20 = 5000 - 20x

\implies x + 20x = 5000

\implies 21x = 5000

\implies x = 5000/ 21 = 238.09

∴ CP of the item = Rs 238.09

4). Let CP be Rs x, then,

Loss % = \frac{(x-540)}{x} \times 100

\implies 5 = \frac{(x-540)}{x} \times 100

\implies 5x = 100(x-540)

\implies x = \frac{100}{5} (x-540)

\implies x = 20(x-540) = 20x-20\times 540

\implies 20\times 540 = 20x-x

\implies 19x = 20\times 540 (rearranging)

\implies x = \frac{20\times 540}{19}

\implies x = 560.42

∴ 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 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.

\boxed{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.

Ans). Profit = 5%
(a) CP = Rs 700 + Rs 50 = Rs 750
Let SP be x
Profit % = \frac{(SP- CP)}{CP}\times 100
\implies 5 = (x-750)750 \times 100
\implies 5\times 75 = 10(x-750)
\implies 10(x-750) = 5\times 75 (rearranging)
\implies x-750 = \frac{5\times 75}{10} = 37.5
\implies x = 37.5 + 750 = 787.5
∴ SP of the item = Rs 787.50

(b) CP = Rs 1150 + Rs 50 = Rs 1200
Let SP be x
Profit % = \frac{(SP- CP)}{CP}\times 100
\implies 5 = \frac{(x-1200)}{1200} \times 100
\implies 5\times 12 = (x-1200)
\implies x-1200 = 5\times 12 (rearranging)
\implies x-1200 = 60
\implies x = 60 + 1200 = 1260
∴ SP of the item = Rs 1260

(b) CP = Rs 560 + Rs 40 = Rs 600
Let SP be x
Profit % = \frac{(SP- CP)}{CP}\times 100
\implies 5 = \frac{(x-600)}{600}\times 100
\implies 5\times 6 = (x-600)
\implies x-600 = 5\times 6 (rearranging)
\implies x-600 = 30
\implies x = 30 + 600 = 630
∴ SP of the item = Rs 630

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