Question
The discount series 10%, 20%, 40% is equivalent to a single discount of = ?
Answer: Option B
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%
$$\eqalign{
& = 28 + 40 - \frac{{28 \times 40}}{{100}} \cr
& = 56.8\% \cr} $$
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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%
$$\eqalign{
& = 28 + 40 - \frac{{28 \times 40}}{{100}} \cr
& = 56.8\% \cr} $$
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