Question

The CP of an object is 750. The loss is \[\dfrac{1}{3}\] of CP. Find SP.

Answer 1

Hint:
Here, we need to find the selling price of the object. The selling price of an object is the price at which the object is sold at. We will use the cost price to find the loss. The cost price of an object is the price at which the object is purchased. The loss is the difference between the cost price and the selling price of an object, if the cost price is greater than the selling price.
Formula Used: We will be using the formula \[{\rm{Loss}} = {\rm{CP}} - {\rm{SP}}\], where CP is the cost price and SP is the selling price.

Complete step by step solution:
We know that the cost price is 750 and the loss is \[\dfrac{1}{3}\] of CP.
We can find the loss by multiplying \[\dfrac{1}{3}\] by 750.
\[\begin{array}{l}{\rm{Loss}} = \dfrac{1}{3} \times 750\\ = 250\end{array}\]
Therefore, we get the loss on the sale of the object as 250.
Next, we will use the amount of loss and the cost price to find the selling price using the formula \[{\rm{Loss}} = {\rm{CP}} - {\rm{SP}}\].
Substituting the loss as 250 and the cost price as 750 in the formula, we get
\[250 = 750 - {\rm{SP}}\]
We can rewrite the equation such that SP is positive.
\[{\rm{SP}} = 750 - 250\]
Simplifying the equation, we get the selling price as
\[{\rm{SP}} = 500\]

\[\therefore\] We get the selling price of the object as 500.

Note:
When an object is sold at a lower price than its cost price, then there will be loss. If the selling price of an object is greater than the cost price, then there will be profit. If in the question, instead of loss, profit was given then we would have used the formula \({\rm{Profit}} = {\rm{SP}} - {\rm{CP}}\). The profit and loss depends on the selling price only.
For example, if a seller buys a pen for 5 rupees and sells the same pen for 10 rupees, then he will get a profit of 5 rupees. Whereas, when he sells the same pen for 3 rupees instead of 10 rupees, then he will incur a loss of 2 rupees.