Prices Related to an Item or Buying and Selling
The buying price of any item is known as its cost price. It is written in short as CP.
The price at which you sell is known as the selling price or in short SP.
What would you say is better, to you sell the item at a lower price, same price or higher price than your buying price? 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
Let us try to interpret the statements related to prices of items.
A toy bought for ₹ 72 is sold at ₹ 80.
A T-shirt bought for ₹ 120 is sold at ₹ 100.
A cycle bought for ₹ 800 is sold for ₹ 940.
Let us consider the first statement.
The buying price (or CP) is ₹ 72 and the selling price (or SP) is ₹ 80.
This means SP is
Hence profit made = SP – CP = ₹ 80 – ₹ 72 = ₹
The profit or loss can be converted to a percentage. It is always calculated on the CP.
For the above examples, we can find the profit % or loss %.
Example :Let us consider the example related to the toy. We have CP = ₹ 72, SP = ₹ 80, Profit = ₹ 8. To find the percentage of profit.
- Profit % = (
/ ) x 100 - Using the formula, we get percent of profit =
% - Substituting the values
- Therefore, We have found the answer.
Similarly you can find the loss per cent in the second situation. Here,
CP = ₹ 120, SP = ₹ 100.
Therefore, Loss = ₹ 120 – ₹ 100 = ₹
Loss per cent =
=
=
On ₹ 120, the loss is ₹ 20 So on 100, the loss =
=
Thus, loss per cent is 16
Try the last case.
Now we see that given any two out of the three quantities related to prices that is, CP, SP, amount of Profit or Loss or their percentage, we can find the rest.
Example 12:The cost of a flower vase is ₹ 120. If the shopkeeper sells it at a loss of 10%, find the price at which it is sold.
- Loss % = (
/ ) × 100 - Using the formula, we get loss = Rs.
- Substituting the values
- Now, we know: Loss =
- - Therefore SP = CP – Loss = Rs.
- Substituting the values
- We have found the answer.
Example 13: Selling price of a toy car is ₹ 540. If the profit made by shopkeeper is 20%, what is the cost price of this toy?
1. A shopkeeper bought a chair for ₹ 375 and sold it for ₹ 400. Find the gain Percentage.
We have, SP = 400 , CP =
So, SP - CP = 400 - 375 =
Since SP > CP Therefore, Gain(%) =
2. Cost of an item is ₹ 50. It was sold with a profit of 12%. Find the selling price.
CP = Rs
Therefore, SP = CP(1+
Put the values in the above equation, we get = 50(1+
3. An article was sold for ₹ 250 with a profit of 5%. What was its cost price?
We have, SP = Rs 250, Profit =
Therefore, SP = CP (1+
put the values in the above equation, we get = CP =
4. An item was sold for ₹ 540 at a loss of 5%. What was its cost price?
We have, SP = Rs
Therefore, SP = CP (1-
put the values in the above equation, we get = CP =