​The cost price of 28 articles is the same as the selling price of x articles. If the profit is 40%, then find the value of x. ​

Correct option is B

Given:

The cost price of 28 articles is the same as the selling price of x articles.

The profit is 40%.

Formula Used:
Profit percentage is calculated as:

​$$\text{Profit percentage} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\%$$​​

Solution:​

Let the cost price of 1 article be C.

Let the selling price of 1 article be S.

Given that the profit is 40%, we can write the selling price as:

S = C + 0.4C = 1.4C

The cost price of 28 articles is 28C, and the selling price of x articles is x S.

28C = $$x \times 1.4C$$​​

Simplify the equation:

28C = 1.4xC

28 = 1.4x

x = $$\frac{28}{1.4}$$​= 20

Thus, the correct option is (b) 20

Alternate Method:

28 CP  = x SP

$$\frac{SP}{CP}$$ $$= \frac{28}{x}$$    .......(I)

Since Profit  = 40%

=> CP    :     SP

100   :    140

Putting value in Equation (i):

​$$\frac{140}{100} = \frac{28}{x}$$ 

x = $$\frac{28 \times 10}{14}$$ 

x = 20