# Profit or Loss as a Percentage

## Definition

Cost Price(C.P.): The buying price of any item is known as its cost price.

Selling Price(S.P): The price at which you sell any item is known as the selling price.

Profit: Profit is the revenue remaining after all costs are paid from selling price.

Loss: When the item is sold and the selling price is less than the cost price, then it is said, the seller has incurred a loss.

## Formula

Profit = Selling Price - Cost Price, which means CP < SP.

Loss = Cost Price - Selling Price, which means CP > SP.

Profit Percent = "Profit"/"Cost Price" xx 100.

Loss Percent = "Loss"/"Cost Price" xx 100.

## Notes

### Profit Or Loss as a Percentage:

Cost Price(C.P.): The buying price of any item is known as its cost price. It is written in short as CP.

Selling Price(S.P): The price at which you sell any item is known as the selling price. It is written in short as SP.

Profit: Profit is the revenue remaining after all costs are paid from selling price.

Loss: When the item is sold and the selling price is less than the cost price, then it is said, the seller has incurred a loss.

You can decide whether the sale was profitable or not depending on the CP and SP.

• If CP < SP then you made a profit = SP – CP.
• If CP = SP then you are in a no-profit no loss situation.
• If CP > SP then you have a loss = CP – SP.

The profit or loss can be converted to a percentage.

It is always calculated on the CP.

• Profit Percent = "Profit"/"Cost Price" xx 100.

• Loss Percent = "Loss"/"Cost Price" xx 100.

## Example

The cost of a flower vase is Rs. 120. If the shopkeeper sells it at a loss of 10%, find the price at which it is sold.

Given: CP = Rs. 120 and Loss percent = 10.

Loss of 10% means if CP is Rs. 100, Loss is Rs. 10

Therefore,

SP would be Rs.(100 - 10) = Rs. 90

When CP is Rs. 100, SP is Rs. 90.

Therefore, if CP were Rs. 120 then
SP = 90/100 xx 120 = Rs. 108.

Given: CP = Rs. 120 and Loss percent = 10.

Loss is 10% of the cost price

= 10% of Rs. 120

= 10/100 xx 120

= Rs. 12

Therefore,

SP = CP - Loss = Rs. 120 - Rs. 12 = Rs. 108

## Example

Selling price of a toy car is Rs. 540. If the profit made by the shopkeeper is 20%, what is the cost price of this toy?

Given: SP = Rs. 540 and the Profit = 20%.

20% profit will mean if CP is Rs. 100, profit is Rs. 20.

Therefore, SP = 100 + 20 = 120

Now, when SP is Rs. 120, then CP is Rs. 100.

Therefore, when SP is Rs. 540,

Then CP = 100/120 xx 540 = Rs. 450.

Given: SP = Rs. 540 and the Profit = 20%.

Profit = 20% of CP and SP = CP + Profit

So, 540 = CP + 20% of CP

= CP + 20/100 xx "CP" = [1 + 1/5]"CP"

= 6/5 "CP".

Therefore, 540 xx 5/6 = CP or Rs. 450 = CP

## Example

Joseph bought a machine for Rs. 23500. He paid Rs. 1200 for transport and Rs. 300 as tax. If he sold it to a customer for Rs. 24250, what was his percent profit or loss?

Total cost price of machine = 23500 + 1200 + 300 = Rs. 25000

Selling price = Rs. 24250
Cost price greater than selling price. Therefore, loss.
Loss = Cost price - Selling price
= 25000 - 24250
= Rs. 750

Joseph suffered a loss of Rs. 750.

Supposing loss was N%,
"N"/100 = 750/25000

∴ "N"/100 xx 100 = 3/100 xx 100

∴ N = 3
∴ Loss = 3%

## Example

Saritaben bought 18 chairs each at Rs. 700 and sold them all for Rs. 18900. What was the percentage of her profit or loss?

Cost price of one chair Rs. 700.
∴ Cost price of 18 chairs = 700 × 18 = Rs. 12600.

Total selling price of all chairs, Rs. 18900.
Selling price more than cost price.
Therefore,
Profit = Selling price - Cost price
= 18900 - 12600
= 6300

Saritaben made a profit of Rs. 6300.

Supposing profit was N%.

"N"/100 = 6300/12600

∴ "N"/100 xx 100 = 63/126 xx 100

∴ N = (63 xx 100)/126

∴ N = 50

∴ Profit was 50%.

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