Question
The single discount equal to three consecutive discounts of 10%, 12% and 5% ?
Answer: Option C
Let the marked price Rs. 100
$$\eqalign{
& {\text{Final selling price}} \cr
& {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{88}}{{100}} \times \frac{{95}}{{100}} \cr
& {\text{ = Rs}}{\text{. 75}}{\text{.24 }} \cr
& {\text{Net discount }} \cr
& {\text{ = }}\left( {100 - 75.24} \right) \cr
& {\text{ = 24}}{\text{.76}}\% \cr} $$
Alternate :
Single equivalent discount for 10% and 12%
$$\eqalign{
& = \left( {10 + 12 - \frac{{10 \times 12}}{{100}}} \right)\% \cr
& = 20.8\% \cr} $$
Single equivalent discount for 20.8% and 5%
$$\eqalign{
& = \left( {20.8 + 5 - \frac{{20.8 \times 5}}{{100}}} \right)\% \cr
& = 24.76\% \cr} $$
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Let the marked price Rs. 100
$$\eqalign{
& {\text{Final selling price}} \cr
& {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{88}}{{100}} \times \frac{{95}}{{100}} \cr
& {\text{ = Rs}}{\text{. 75}}{\text{.24 }} \cr
& {\text{Net discount }} \cr
& {\text{ = }}\left( {100 - 75.24} \right) \cr
& {\text{ = 24}}{\text{.76}}\% \cr} $$
Alternate :
Single equivalent discount for 10% and 12%
$$\eqalign{
& = \left( {10 + 12 - \frac{{10 \times 12}}{{100}}} \right)\% \cr
& = 20.8\% \cr} $$
Single equivalent discount for 20.8% and 5%
$$\eqalign{
& = \left( {20.8 + 5 - \frac{{20.8 \times 5}}{{100}}} \right)\% \cr
& = 24.76\% \cr} $$
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