Question

Find the single discount which is equivalent to two successive discounts of $20\%$ and $5\%$.

Answer 1

Step 1: Find the price after the given two successive discounts

Let the marked price of an article be $\mathrm{Rs}.\mathrm{x}$.

First discount of $20\%$ on it is,

$$\begin{gathered} =0.2\left(\mathrm{x}\right) \\ =\mathrm{Rs}.0.2\mathrm{x} \end{gathered}$$.

Price after discount is

$$\begin{gathered} =x-0.2x \\ =Rs.0.8x \end{gathered}$$

So, the second discount of $5\%$ on the reduced price is

$0.8x\times \frac{5}{100}=Rs.0.04x$

So, the price after the second discount is

$$\begin{gathered} =\mathrm{Rs}.\left(0.8\mathrm{x}-0.04\mathrm{x}\right) \\ =\mathrm{Rs}.0.76\mathrm{x} \end{gathered}$$.

Step 2: Find the single discount

Single discount is equivalent to

$\begin{array}{rcl}\frac{\left(x-0.76x\right)}{x}\times 100& =& \frac{0.24x}{x}\times 100\\ & =& 24\%\end{array}$

Hence, the equivalent single discount is $24\%$.