By selling article at $$\frac{2}{5}$$ of its actual selling price, Manav incures a loss of 27%. If he sells it at 84% of its actual selling price, then the profit percentage is:

Correct option is D

Given:

By selling article at $$\frac{2}{5}$$ of its actual selling price,

Manav insures a loss of 27%.

He sells it at 84% of its actual selling price

Formula used: 

SP - CP = Profit

Solution :

Selling price = $$\frac{2}{5}x$$ 

$$Selling \ Price = C.P - 0.27 \times C.P = 0.73 \times C.P$$ 

$$\frac{2}{5} x = 0.73 \times C.P$$ 

Solving for the cost price (C.P.):

$$C.P = \frac{2x}{5 \times 0.73} = \frac{2x}{3.65}$$ 

Selling Price = 0.84x

$$Profit = 0.84x - \frac{2x}{3.65}$$ 

​Profit Percentage =​

$$0.84x - \frac{2x}{3.65}$$ $$\div$$ $$\frac{2x}{3.65}$$ $$\times 100$$

$$=$$ $$\frac{0.84 \times 3.65 - 2}{2}$$ $$\times 100$$ 

$$0.84 \times 3.65 = 3.006$$ 

$$3.006 - 2 = 1.066$$ 

$$Profit \ percentage = \frac{1.066}{2} \times 100 = 53.3$$% 

The profit percentage is 53.3%