A single discount equivalent to the successive discounts of 10%, 20% and 25% is = ?

Solution(By Examveda Team)

Let the price is = Rs. 100
After discount price
$$\eqalign{ & {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{80}}{{100}} \times \frac{{75}}{{100}} \cr & {\text{ = Rs}}{\text{. 54}} \cr & {\text{Difference = 100}} - 54 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 46\% \cr} $$
So, 46% 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 25%
$$\eqalign{ & = 28 + 25 - \frac{{28 \times 25}}{{100}} \cr & = 46\% \cr} $$