If the discount is equal to one fifth of the marked price and the loss is half the discount, then the percentage of loss is = ?

Solution(By Examveda Team)

Let the marked price = Rs. 100
$$\eqalign{ & {\text{Discount}} = \frac{1}{5} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}20 \cr & {\text{Loss = }}\frac{1}{2} \times 20 \cr & \,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 10}} \cr & {\text{Cost price}} = 100 - 20 + 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 90}} \cr & {\text{Loss}}\% = \frac{{10}}{{90}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{9}\% {\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% {\text{ }} \cr} $$