Question
The equivalent single discount for two successive discounts of 15% and 10% is = ?
Answer: Option C
Equivalent to a single discount
$$\eqalign{
& = 15 + 10 - \frac{{15 \times 10}}{{100}} \cr
& = 25 - 1.5 \cr
& = 23.5\% \cr} $$
Alternate :
$$\eqalign{
& {\text{Market price = Rs}}{\text{.100}} \cr
& {\text{Cost price}} \cr
& {\text{ = 100}} \times \frac{{85}}{{100}} \times \frac{{90}}{{100}} \cr
& {\text{ = Rs}}{\text{. }}76.5 \cr
& {\text{Difference = 100}} - 76.5 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23.5 \cr
& {\text{Difference}}\% \cr
& = \frac{{23.5}}{{100}} \times 100 \cr
& = 23.5\% \cr} $$
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Equivalent to a single discount
$$\eqalign{
& = 15 + 10 - \frac{{15 \times 10}}{{100}} \cr
& = 25 - 1.5 \cr
& = 23.5\% \cr} $$
Alternate :
$$\eqalign{
& {\text{Market price = Rs}}{\text{.100}} \cr
& {\text{Cost price}} \cr
& {\text{ = 100}} \times \frac{{85}}{{100}} \times \frac{{90}}{{100}} \cr
& {\text{ = Rs}}{\text{. }}76.5 \cr
& {\text{Difference = 100}} - 76.5 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23.5 \cr
& {\text{Difference}}\% \cr
& = \frac{{23.5}}{{100}} \times 100 \cr
& = 23.5\% \cr} $$
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