Question

Find the single discount equivalent to two successive discounts of $20\%$ and $10\%$.

Answer 1

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

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

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

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

Price after discount is

$$\begin{gathered} =\mathrm{Rs}.\left(\mathrm{x}-0.2\mathrm{x}\right) \\ =\mathrm{Rs}.0.8\mathrm{x} \end{gathered}$$

So, second discount of $10\%$ on the price is

$0.8\mathrm{x}\times \frac{10}{100}=\mathrm{Rs}.0.08\mathrm{x}$

So, the price after second discount $0.8x-0.08x=\mathrm{Rs}.0.72x$.

Step 2: Find the single equivalent discount

Single discount equivalent is given as

$\begin{array}{rcl}\frac{\left(x-0.72x\right)}{\mathrm{x}}\times 100& =& \frac{0.28x}{\mathrm{x}}\times 100\\ & =& 28\%\end{array}$

Hence, the single discount equivalent is $28\%$.