Question

Find SP, if CP=Rs.60 and loss\[ = 12\dfrac{1}{2}\% \]

Answer 1

Hint: When a product is purchased in the view of selling it to the consumer in order to do business then, the price in which the product is bought by the seller is known as the cost price of the product and the price in which the seller sells the product to the consumer is known as selling of the product for the seller. If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. Profit percent or loss percent of a product is always calculated on the cost price of the product.

Complete step-by-step answer:
In this question, the cost price has been given, and the seller has suffered a loss; hence we need to find the selling price. So using the formula for the loss, we can get the result.
Given Cost Price (CP)\[ = Rs.60\]
Loss\[ = 12\dfrac{1}{2}\% = \dfrac{{25}}{2}\% \]
Since by selling an item, the seller has suffered a loss, we can say the selling price must have been less than the cost price,
The loss percentage for an item is given by the formula

\[L\% = \dfrac{{C.P - S.P}}{{C.P}} \times 100\]
Now substitute the values in the formula we get
\[
  \dfrac{{25}}{2} = \left( {1 - \dfrac{{SP}}{{CP}}} \right) \times 100 \\
  \dfrac{{25}}{{200}} = 1 - \dfrac{{SP}}{{CP}} \\
  \dfrac{{SP}}{{CP}} = 1 - \dfrac{1}{8} \\
  \dfrac{{SP}}{{CP}} = \dfrac{7}{8} \\
 \]
By further solving, we get
\[
  SP = \dfrac{7}{8} \times CP \\
   = \dfrac{7}{8} \times 60 \\
   = Rs.52.5 \\
 \]
Hence the selling price of the item\[ = Rs.52.5\]

Note: It is to be noted here that many a time, the marked price has been given in the question instead of selling price. So, be careful while reading the question as the marked price is the price which has been marked on the product by the seller but the selling price is the price of the product which the seller actually gets for the product after discount.