Question

Find a single discount equivalent to following successive discounts :

of 10%, 20% and 20% is (in percent)

Answer 1

Say the Marked Price be Rs. 100 and $d_1$ = 10 %, $d_2$ = 20 % and $d_3$ = 20 %
S.P = $\left(\frac{100-d_1}{100}\right)\times \left(\frac{100-d_2}{100}\right)\times \left(\frac{100-d_3}{100}\right)\times$M.P
= $\left(\frac{100-10}{100}\right)\times \left(\frac{100-20}{100}\right)\times \left(\frac{100-20}{100}\right)\times$ 100
= $\left(\frac{90}{100}\right)\times \left(\frac{80}{100}\right)\times \left(\frac{80}{100}\right)\times$100
= $\left(\frac{576}{1000}\right)\times$100
= Rs. 57.6
The single equivalant discount = M.P - S.P = Rs. 100 - Rs. 57.6 = Rs. 42.4
$\therefore$ single equivalent discount %
= $\left(\frac{singleequivalentdiscount}{M.P}\right)=\frac{42.4}{100}$= 42.4 %
Ans = 42.4 %