Successive Discounts Calculation

To find the single discount equivalent to successive discounts, we calculate the final price after applying both discounts sequentially. Assuming an original price of $100 simplifies the calculation.

First Discount Application (15%)

Let the marked price be $M.P. = 100$. The first discount is $15\%$. Discount amount = $15\%$ of $100 = \frac{15}{100} \times 100 = 15$. Price after the first discount = $M.P. - \text{Discount Amount} = 100 - 15 = 85$.

Second Discount Application (18%)

The second discount of $18\%$ is applied to the reduced price of $85$. Discount amount = $18\%$ of $85 = \frac{18}{100} \times 85 = 0.18 \times 85 = 15.3$. Final price after the second discount = $85 - 15.3 = 69.7$.

Equivalent Single Discount Calculation

The total discount amount is the difference between the original price and the final price. Total Discount Amount = $100 - 69.7 = 30.3$.

The equivalent single discount percentage is calculated as: $ \text{Equivalent Discount %} = \left( \frac{\text{Total Discount Amount}}{\text{Original Price}} \right) \times 100 $ $ \text{Equivalent Discount %} = \left( \frac{30.3}{100} \right) \times 100 = 30.3\% $

Formula for Equivalent Discount

Alternatively, use the formula for equivalent single discount $D$ for successive discounts $d_1$ and $d_2$: $ D = d_1 + d_2 - \frac{d_1 \times d_2}{100} $ Given $d_1 = 15\%$ and $d_2 = 18\%$. $ D = 15 + 18 - \frac{15 \times 18}{100} $ $ D = 33 - \frac{270}{100} $ $ D = 33 - 2.7 $ $ D = 30.3\% $

Thus, the single discount equivalent to successive discounts of 15% and 18% is 30.3%.