The price of an article reduces to 576 after two successive discounts. The markup is 80% above the cost price of Rs. 500. What is the new profit percentage if instead of two successive discounts the markup price was further increased successively two times by the same percentage?

Solution (By Examveda Team)

$$\eqalign{ & {\text{CP}} = 500 \cr & {\text{SP}} = 576 \cr & {\text{MP}} = 900\left[ {80\% \,{\text{above}}\,{\text{the}}\,{\text{CP}}} \right] \cr & {\text{Now}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & \left[ {{\text{R = Rate}}\,{\text{of}}\,{\text{Discount}}} \right] \cr & 576 = 900 \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & R = 20\% \cr & \cr & {\text{Again}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 + {\frac{R}{{100}}} } \right]^2} \cr & {\text{SP}} = 900 \times {\left[ {1 + {\frac{{20}}{{100}}} } \right]^2} \cr & {\text{SP}} = 1296 \cr & {\text{New}}\,{\text{Profit}}\,{\text{Percentage}}, \cr & = {\frac{{ {SP - CP} }}{{CP}}} \times 100 \cr & = {\frac{{ {1296 - 500} }}{{500}}} \times 100 \cr & = 159.2\% \cr} $$