Question

An article is sold at a certain price. By selling it at $\dfrac{2}{3}$ that price one loses 10%. Find the gain percent at original price.
$
  {\text{A}}{\text{. 31% }} \\
  {\text{B}}{\text{. 23% }} \\
  {\text{C}}{\text{. 35% }} \\
  {\text{D}}{\text{. 45% }} \\
$

Answer 1

Hint: To find the gain percent we use the cost price formula. Also we use the relationship between Cost Price, Selling Price and Gain.

Complete step-by-step answer:

Let, CP = Cost Price and SP = Selling Price

Let the original selling price be x

The new selling price is: ($\dfrac{2}{3}$) of x = $\dfrac{{2{\text{x}}}}{3}$

We know CP = $\dfrac{{100}}{{100 - {\text{loss}}}} \times {\text{SP}}$

Here, Loss = 10% and SP = $\dfrac{{2{\text{x}}}}{3}$

Now CP =$\dfrac{{100}}{{100 - 10}} \times \dfrac{{2{\text{x}}}}{3} = \dfrac{{{\text{20x}}}}{{27}}$ . This is the Cost Price for that article.

Selling Price is: x

Gain = Selling Price - Cost Price
           = $x$ - $\dfrac{{{\text{20x}}}}{{27}}$= $\dfrac{{{\text{7x}}}}{{27}}$

Now Gain% = $\dfrac{{{\text{7x}}}}{{27}}$×$\dfrac{{{\text{20x}}}}{{27}}$ x 100 = 35% --- (Gain % = Gain × CP × 100)
Hence Option C is the correct answer.

Note: In order to solve this type of questions the key is to know the Cost price formula and relation between CP and SP and Gain and Gain Percentage. We consider a variable x, using the given data we form a relation with only one variable, solve it for answer.