Question

A single discount(as percent) equivalent to $20\%,10\%$ and $5\%$ is $31.6\%.$

• A. True
• B. False

Answer 1

The correct option is A True

Let CP and SP be the original Cost Price and Selling Price of an item

applying Discount D1 $\left(20\%\right)$ we get,

$S{P}_1=CP-\frac{20}{100}\times CP$

$=\frac{4}{5}\times CP=C{P}_1$

Applying Discount D2$\left(10\%\right)$

$S{P}_2=C{P}_1-\frac{10}{100}\times C{P}_1$

$=\frac{9}{10}\times C{P}_1=C{P}_2$

Applying Discount D3$\left(5\%\right)$

$S{P}_3=C{P}_2-\frac{5}{100}\times C{P}_2$

$=\frac{95}{100}\times C{P}_2$

Final Seliing Price $=\frac{95}{100}\times C{P}_2$

$=\frac{171}{250}\times CP$

$SP=\frac{171}{250}\times CP$

$=CP-\frac{79}{250}\times CP$

$SP=CP-\frac{31.6}{100}\times CP$

$\therefore$ a single discount would be $31.6$ and hence the statement is True.