Question

Find the single discount (as percent) equivalent to successive discounts of :

$\left(i\right)80\%$ and $80\%$

$\left(ii\right)60\%$ and $60\%$

$\left(iii\right)60\%$ and $80\%$

Answer 1

$\left(i\right)$ Successive discounts$=80\%$ and $80\%$
Let $M.P.=Rs.100$
Then $S.P.$ after two discounts
$=Rs.\frac{100(100-80)\times (100-80)}{100\times 100}$
$=Rs.(\frac{100\times 20\times 20}{100\times 100)}=Rs.4$
$\therefore$ Total discounts $=Rs.100-4=Rs.96$
$\therefore$ Single discount$=Rs.96\%$

$\left(ii\right)$ Successive discounts $=60\%$ and $60\%$
Let $M.P.=Rs.100$
Then $S.P$ after two discounts,
$=\left(\frac{100(100-60)(100-60)}{100\times 100}\right)$
$=\left(\frac{100\times 40\times 40}{100\times 100}\right)$

$=Rs.16$
$\therefore$ Total discount $=Rs.100-16=Rs.84$
Single discount $=84\%$

$\left(iii\right)$ Successive discounts $=60\%$ and $80\%$
Let $M.P.=Rs.100$
$\therefore$ $S.P.$ after two discounts
$=Rs.\left(\frac{100(100-60)(100-80)}{100\times 100}\right)$
$=Rs.\left(\frac{100\times 40\times 20}{100\times 100}\right)$

$=Rs.8$
$\therefore$ Total discount $=Rs.100-8=Rs.92$
$\therefore$ Single discount $=92\%$