The discount series 10%, 20%, 40% is equivalent to a single discount of = ?

Solution(By Examveda Team)

Let the price is = Rs. 100
After discount price
$$\eqalign{ & {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{80}}{{100}} \times \frac{{60}}{{100}} \cr & {\text{ = Rs}}{\text{. 43}}{\text{.2}} \cr & {\text{Difference = 100}} - 43.2 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 56.8\% \cr} $$
So, 56.8% is a single discount of percent of this series.

Alternate :
Successive discount of 10% of 20%
$$\eqalign{ & = 10 + 20 - \frac{{10 \times 20}}{{100}} \cr & = 28\% \cr} $$
Then successive discount of 28% and 40%
$$\eqalign{ & = 28 + 40 - \frac{{28 \times 40}}{{100}} \cr & = 56.8\% \cr} $$