Question

Find a single discount equivalent to following successive discounts.

The nearest integer value of 20%, 10% and 5% in percent is:

Answer 1

Say the Marked Price be Rs. 100 and $d_1$ = 20%, $d_2$ = 10 % and $d_3$= 5 %
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
=$\left(\frac{100-20}{100}\right)\times \left(\frac{100-10}{100}\right)\times \left(\frac{100-5}{100}\right)\times$ 100
=$\left(\frac{80}{100}\right)\times \left(\frac{90}{100}\right)\times \left(\frac{95}{100}\right)\times$100
=$\left(\frac{684}{1000}\right)\times$100
= Rs. 68.4
the single equivalent discount = M.P - S.P
= Rs. 100 - Rs. 68.4 = Rs. 31.6
$\therefore$The single equivalent discount % = $\left(\frac{singleequivalentdiscount}{M.P}\right)=\frac{31.6}{100}=31.6$ %
Ans = 31.6 %