Question

Find a single discount (as percent) equivalent to following successive discounts : (i) 20% and 12% (ii) 10%, 20% and 20% (iii) 20%, 10% and 5%

Answer 1

(i) Successive discount = 20% and 12%
Let M.P. = rs. 100
First discount = 20%
Second discount = 12%
$\therefore$ S.P. =$\frac{M.P.(100-Discount}{100}$
= $\frac{100\times (100-20)(100-12)}{100\times 100}$
= $\frac{100\times 80\times 88}{100\times 100}=\frac{352}{5}$
$\therefore$ Total discount on Rs. 100= 100 - $\frac{352}{5}$
= $\frac{500-352}{5}=Rs.\frac{148}{5}$
$\therefore$ Single discount = $\frac{148}{5}$%
(ii) Successive discounts 10%, 20% and 20%
Let M.P. = Rs. 100
$\therefore$ S.P. after 3 discounts
= $\frac{100(100-10)(100-20)(100-20)}{100\times 100\times 100}$
= $\frac{100\times 90\times 80\times 80}{100\times 100\times 100}=\frac{576}{10}$
$\therefore$ Total discount = Rs. $100-\frac{576}{10}$
= Rs. $\frac{1000-576}{10}=\frac{424}{10}$
$\therefore$ Single discount = $\frac{424}{10}$% = 42.4%
(iii) Successive discounts = 20%, 10%, 5%
Let M.P. = Rs. 100
\therefore S.P. after three discounts
= Rs. $\frac{100(100-20)(100-10)(100-5)}{100\times 100\times 100}$
= Rs. $\frac{100\times 80\times 90\times 95}{100\times 100\times 100}=Rs.\frac{342}{5}$
$\therefore$ Total discount = $100-\frac{342}{5}$
= $\frac{500-342}{5}=\frac{158}{5}$
$\therefore$ Single discount = $\frac{158}{5}$% = 31.6%