​By selling an article at $$\frac38$$​ of its actual selling price, Sharad incurs a loss of 19%. If he sells it at 60% of its actual selling price, then ....................​

Correct option is D

Given:

Selling Price $$= \frac{3}{8}$$​ of Selling Price

Loss = 19%

Formula Used:

Loss = CP - SP

Loss Percent = $$\frac{Loss}{CP} \times 100$$​​

Solution:

Let the actual selling price be x

Then selling price will be = $$\frac{3}{8} of x = \frac{3x}{8}$$​​

Let the cost price be y

Then loss = 19% of y = 0.19y

Selling price = y - 0.19y = 0.81y

And $$0.81y = \frac{3x}{8}$$​​

​$$y = \frac{3x}{8} \times \frac{1}{0.81} =\frac{25x}{54}$$​​

Cost Price = $$\frac{25x}{54}$$​​

If article is sold at 60% of actual price then:

Actual selling price = 60% of x = $$\frac{3x}{5}$$​​

Profit = $$\frac{3x}{5} - \frac{25x}{54}= \frac{162x - 125x}{270} = \frac{37x}{270}$$​​

Profit Percent = $$\frac{\left(\frac{37x}{270}\right)}{\left(\frac{25x}{54}\right)} \times 100 = 29.6\%$$​​