True Discount - Aptitude MCQ Questions and Solutions with Explanations

Let cost price of article = Rs. 100
Marked of each article
$$\eqalign{ & {\text{ = }}\frac{{130}}{{100}} \times {\text{100 }} \cr & {\text{ = Rs}}{\text{. 130}} \cr} $$
For first 2 items, S.P. = 130 × 2 = 260
For the next item, discount = 15%
$$ \Rightarrow \frac{{15}}{{100}} \times 130 = 19.5$$
$$⇒$$ S.P. for the next item = 130 - 19.5 = 110.5
Discount for final item = 30%
$$ \Rightarrow \frac{{30}}{{100}} \times 130 = 39$$
$$⇒$$ S.P. for final item = 130 - 39 = 91
Let number of article to be sold = 4 at the rate of Rs. 130 each
= Total selling price
= 260 + 110.5 + 91 = Rs. 461.5
Total cost price = 4 × 100 = 400
$$\eqalign{ & \Leftrightarrow {\text{Profit }}\% \cr & = \frac{{461.5 - 400}}{{400}} \times 100 \cr & = {\text{ }}15\frac{3}{8}\% \cr} $$

Let the cost price of bag is = 100 units
∴ Marked price of the bag = 150 units
Selling price of the bag :
$$\eqalign{ & 150 \times \frac{{80}}{{100}} = 120{\text{ units}} \cr & {\text{120 units = Rs. 840}} \cr & {\text{1 units = 7}} \cr & {\text{100 units = Rs. 700}} \cr} $$

Cost price of the article = Rs. 8000
Profit% = 12%
Selling price of the article
$$\eqalign{ & {\text{ = Cost price}} \times \frac{{100 + {\text{P}}\% }}{{100}}{\text{ }} \cr & = 8000 \times \frac{{112}}{{100}} \cr & {\text{ = Rs}}{\text{. 8960}} \cr} $$
$$\eqalign{ & \therefore {\text{ Discount }} \cr & {\text{ = Marked price}} - {\text{Selling price}} \cr & {\text{ = 11200}} - {\text{8960 }} \cr & {\text{ = Rs}}{\text{. 2240}} \cr} $$
Let the discount percentage = x%
$$\eqalign{ & \therefore \frac{{11200 \times x}}{{100}} = 2240 \cr & \Rightarrow x = \frac{{2240 \times 100}}{{11200}} \cr & \Rightarrow x = 20\% \cr} $$

Alternate :
$$\eqalign{ & \frac{{100 - {\text{D}}\% }}{{100 + {\text{P}}\% }} = \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} \cr & \Rightarrow \frac{{100 - x}}{{100 + 12}} = \frac{5}{7} \cr & \Rightarrow \frac{{100 - x}}{{112}} = \frac{5}{7} \cr & \Rightarrow 700 - 7x = 560 \cr & \Rightarrow 7x = 700 - 560 \cr & \Rightarrow x = \frac{{140}}{7} \cr & \Rightarrow x = 20\% \cr} $$

Let the marked price = 100x
Shop Keeper gives 5% discount, therefore, Price becomes = 95x
Again if shopkeeper gives 6% discount then the price become = 94x
According to the question if he gives 6% discount his earning will Rs.15 less
∴ 95x - 94x = 15
⇒ x = 15
∴ Marked price = 100 × 15 = Rs. 1500

$$\eqalign{ & {\text{Discount }}\% \cr & = \frac{{440 - 396}}{{440}} \times 100 \cr & = 10\% \cr} $$

$$\eqalign{ & {\text{Let, Marked price = Rs}}{\text{. }}x \cr & \therefore x \times \frac{{70}}{{100}} \times \frac{{85}}{{100}} = 476 \cr & \Rightarrow x = 476 \times \frac{{100}}{{70}} \times \frac{{100}}{{85}} \cr & \Rightarrow x = {\text{Rs}}{\text{. }}800 \cr} $$

$$\eqalign{ & {\text{True}}\,{\text{Discount}}\, = \,{\text{Rs}}{\text{. 150}} \cr & {\text{and}} \cr & {\text{Simple}}\,{\text{interest}}\, = \,{\text{Rs}}{\text{.}}\,{\text{200}} \cr & {\text{Sum}}\,{\text{due}}\, = \,\frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{TD}}}}{{\left( {{\text{S}}{\text{.I}}{\text{.}}} \right) - \left( {{\text{TD}}} \right)}} \cr & = \,{\text{Rs}}{\text{.}}\left( {\frac{{200 \times 150}}{{200 - 150}}} \right) \cr & = \,{\text{Rs}}. 600 \cr & \therefore {\text{Rate}} \cr & \, = \,\left( {\frac{{100 \times 200}}{{600 \times \frac{8}{3}}}} \right)\% \cr & = \,\left( {\frac{{20000}}{{1600}}} \right)\% \cr & = \,\left( {\frac{{200}}{{16}}} \right)\% \cr & = \,12\frac{1}{2}\% \cr} $$

$$\eqalign{ & {\text{Cost price for the retailer }} \cr & = 800 \times \frac{{90}}{{100}} \times \frac{{85}}{{100}} + 13 \cr & = 612 + 13 \cr & {\text{ = Rs. 625 }} \cr & {\text{Selling price = Rs}}{\text{. 875}} \cr & \therefore {\text{Profit }}\% {\text{ }} \cr & = \frac{{875 - 625}}{{625}} \times 100 \cr & = \frac{{250}}{{625}} \times 100 \cr & = 40\% \cr} $$

Let the number of visitors in the beginning = 100
$$\eqalign{ & {\text{Total revenue}} \cr & = 0.25 \times 100 \cr & = {\text{Rs}}{\text{. 25}} \cr & {\text{New price}} \cr & = 25 \times \frac{{80}}{{100}} \cr & = 0.20{\text{ or 20 paise}} \cr & {\text{New revenue}} \cr & = 25 \times \frac{{128}}{{100}} \cr & = {\text{Rs}}{\text{. 32}} \cr & {\text{Number of visitors now}} \cr & = \frac{{32}}{{0.20}} \cr & = 160 \cr & {\text{Change in number of visitor }}\% \cr & = \frac{{160 - 100}}{{100}} \times 100 \cr & = 60\% \cr} $$

Let the cost price = 100 units
Marked price = 140 units
Selling price = 140 × $$\frac{{85}}{{100}}$$   = 119
$$\eqalign{ & {\text{Profit }}\% = \frac{{19}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr} $$