True Discount — Part 2 MCQs with Explanations

Selling price of grinder = Rs. 1955 $$\eqalign{ & {\text{Cost price of grinder}} \cr & {\text{= 1955}} \times \frac{{100}}{{115}} \cr & = {\text{Rs}}{\text{. 1700}} \cr & {\text{Marked price of grinder}} \cr & {\text{= 1700}} \times \frac{{100}}{{85}} \cr & = {\text{Rs}}{\text{. 2000}} \cr & {\text{Discount by the retailer }} \cr & {\text{= 2000}} \times \frac{{15}}{{100}} \cr & = {\text{Rs}}{\text{. 300}} \cr} $$

Marked price of T.V. = Rs. 16000 $$\eqalign{ & {\text{After 1st discount}} \cr & {\text{ = 95}}\% {\text{ of 16000}} \cr & {\text{ = }}\frac{{95}}{{100}} \times 16000 \cr & {\text{ = Rs}}{\text{. 15200}} \cr} $$ Selling price of T.V. = Rs. 11400 $$\eqalign{ & {\text{ So, the 2nd discount be}}\% \cr & = \frac{{15200 - 11400}}{{15200}} \times 100 \cr & = \frac{{3800}}{{15200}} \times 100 \cr & = 25\% \cr} $$

1st discount = 30% Two successive discount to a single discount $$\eqalign{ & = 25 + 5 - \frac{{25 \times 5}}{{100}} \cr & = 30 - 1.25 \cr & {\text{Difference}}\% {\text{ }} \cr & = {\text{ }}30 - 30 + 1.25 \cr & = {\text{ }}1.25\% \cr & {\text{Difference amount}} \cr & = 1.25\% \,{\text{of }}2000 \cr & = \frac{{1.25}}{{100}} \times 2000 \cr & = {\text{Rs}}{\text{. }}25 \cr} $$

Let the marked price = Rs. x Single Discount = 30% Two successive discount is equivalent $$\eqalign{ &{\text{= }}\left( {20 + 10 - \frac{{20 \times 10}}{{100}}} \right)\% \cr & = \left( {30 - 2} \right)\% \cr & = 28\% \cr} $$ Difference = 2% According to the question, $$\eqalign{ & \Rightarrow {\text{2}}\% {\text{ of }}x{\text{ = 72}} \cr & \Rightarrow \frac{2}{{100}} \times x = 72 \cr & \Rightarrow x = \frac{{72 \times 100}}{2} \cr & \Rightarrow x = {\text{Rs}}{\text{. 3600}} \cr} $$

\[\begin{gathered} \begin{array}{*{20}{c}} {{\text{Cost Price}}}&{{\text{Selling Price}}}&{{\text{Mark Price}}} \\ {{{10}_{ \times 20}}}&{}&{{{13}_{ \times 20}}} \\ {}&{{{17}_{ \times 13}}}&{{{20}_{ \times 13}}} \end{array} \hfill \\ \overline {\underline {{\text{ 200 unit}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{221 unit}}\,\,\,\,\,\,\,\,\,\,\,\,{\text{260 unit}}} } \hfill \\ \end{gathered} \] $$\eqalign{ & 221{\text{ unit }} \to {\text{ 910}} \cr & {\text{260 unit }} \to \frac{{910}}{{221}} \times 200 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs 823}}{\text{.50}} \cr} $$

Two successive discount is equivalent $$\eqalign{ & = 20 + 5 - \frac{{20 \times 5}}{{100}} \cr & = {\text{ }}25 - 1 \cr & = {\text{ }}24\% {\text{ }} \cr} $$

Let cost price of item = Rs. 100 Marked price of item = 120% of 100 $$\eqalign{ & {\text{ = }}\frac{{120}}{{100}} \times {\text{100 }} \cr & {\text{ = Rs}}{\text{. 120 }} \cr} $$ After discount, selling price = 87.5% of 120 $$\eqalign{ & \frac{{87.5}}{{100}} \times {\text{120 = Rs}}{\text{. 105}} \cr & {\text{Profit}}\% {\text{ }} = \frac{{105 - 100}}{{100}}{\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{ }}5\% {\text{ }} \cr} $$

Let cost price of item = Rs. 100 Marked price of item = 130% of 100 $$\eqalign{ & {\text{ = 130}}\% {\text{ of 100}} \cr & {\text{ = }}\frac{{130}}{{100}} \times {\text{100 }} \cr & {\text{ = Rs}}{\text{. 130 }} \cr} $$ After discount, selling price $$\eqalign{ & {\text{= 85}}\% {\text{ of 130 }} \cr & = \frac{{85}}{{100}} \times {\text{130 }} \cr & {\text{= Rs}}{\text{. 110}}{\text{.5}} \cr & {\text{Profit}}\% {\text{ }} \cr & = \frac{{110.50 - 100}}{{100}} \times 100{\text{ }} \cr & = 10.5{\text{ }}\% {\text{ }} \cr} $$

Let marked price = 100x, then by statement 95x + 92x → selling price of both $$\eqalign{ & \Rightarrow 187x \to 925 \cr & \Rightarrow x \to \frac{{925}}{{187}} = 4.94 \cr & {\text{Marked price }} \cr & {\text{ = 4}}{\text{.94}} \times {\text{100 }} \cr & {\text{ = Rs}}{\text{. 494}} \cr} $$

Let marked price = Rs. x Selling price after 4% discount $${\text{ = Rs}}{\text{.}}\frac{{96x}}{{100}}$$ $$\eqalign{ & \therefore \frac{{96x}}{{100}} = 1920 \cr & \Rightarrow x = \frac{{1920 \times 100}}{{96}} \cr & \Rightarrow x = {\text{Rs. 2000}} \cr} $$

Let the amount of bill = Rs. x According to the question, $$\eqalign{ & \Rightarrow \frac{{4x}}{{100}} = 13 \cr & x = \frac{{13 \times 100}}{4} \cr & x = {\text{Rs}}{\text{. 325}} \cr} $$ Alternate : Let the amount of bill = 100 units 4% of 100 units = 4 units $$\eqalign{ & \therefore \,{\text{ 4 units}} = {\text{ 13}} \cr & \Rightarrow \,{\text{1 unit}} = \frac{{13}}{4} \cr & \Rightarrow 100\,{\text{units = }}\frac{{13}}{4} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 325}} \cr} $$

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% $$\eqalign{ & = \left( {20.8 + 5 - \frac{{20.8 \times 5}}{{100}}} \right)\% \cr & = 24.76\% \cr} $$

1st discount = 35% Single equivalent discount of 20% each $$\eqalign{ & = \left( {20 + 20 - \frac{{20 \times 20}}{{100}}} \right)\% \cr & = {\text{ }}36\% {\text{ }} \cr & {\text{Difference}} \cr & = \left( {36\% - 35\% } \right) \cr & = 1\% \cr} $$ Let the amount of the bill Rs. x $$\eqalign{ & \therefore \frac{1}{{100}}x = 22 \cr & x = {\text{Rs}}{\text{. }}2200 \cr} $$

A owes = P.W. of Rs. 1573 due $$\frac{3}{2}$$ years hence $$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left[ {\frac{{1573 \times 100}}{{100 + \left( {14 \times \frac{3}{2}} \right)}}} \right]\, \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{1573 \times 100}}{{121}}} \right) \cr & = {\text{Rs}}{\text{.}}\,1300. \cr} $$ B owes = P.W. of Rs. 1444.50 due 6 months hence $$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left[ {\frac{{1444.50 \times 100}}{{100 + \left( {14 \times \frac{1}{2}} \right)}}} \right]\, \cr & = \,{\text{Rs}}{\text{.}}\,\left( {\frac{{1444.50 \times 100}}{{107}}} \right) \cr & = {\text{Rs}}{\text{.}}\,1350. \cr & \therefore \,{\text{B}}\,{\text{must}}\,{\text{pay}}\,{\text{Rs}}{\text{.}}\,\,{\text{50}}\,{\text{to}}\,{\text{A}} \cr} $$

Marked price of watch = Rs. 1600 After 1st discount of 10% $$\eqalign{ & {\text{ = 1600}} \times \frac{{90}}{{100}} \cr & {\text{ = Rs}}{\text{. 1440}} \cr} $$ Customer pays (final selling price) = Rs. 1224 $$\eqalign{ & \frac{x}{{100}} \times 1440 = \left( {1440 - 1224} \right) \cr & \frac{x}{{100}} \times 1440 = 216 \cr & x = \frac{{216 \times 100}}{{1440}} \cr & x = 15\% \cr} $$

Single equivalent discount for 20% and 20% $$\eqalign{ & = 20 + 20 - \frac{{20 \times 20}}{{100}} \cr & = 40 - 4 \cr & = 36\% \cr} $$ Single equivalent discount for 36% and 10% $$\eqalign{ & = 36 + 10 - \frac{{36 \times 10}}{{100}} \cr & = 46 - 3.6 \cr & = 42.4\% \cr} $$

Single equivalent discount for 20% and 10% $$\eqalign{ & = 20 + 10 - \frac{{20 \times 10}}{{100}} \cr & = 30 - 2 \cr & = 28\% \cr} $$ Single equivalent discount for 28% and 5% $$\eqalign{ & = 28 + 5 - \frac{{28 \times 5}}{{100}} \cr & = 33 - 1.4 \cr & = 31.6\% \cr} $$

$$ = \left( {p - q + \frac{{pq}}{{100}}} \right)\% $$

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 $$\eqalign{ & {\text{Profit }}\% = \frac{{19}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr} $$

Let the cost price = 100 units Marked price = 120 units Selling price = 120 × $$\frac{{80}}{{100}}$$ = 96 units There will be loss $$\eqalign{ & {\text{Loss}}\% = \frac{{100 - 96}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\% \cr} $$

$$\eqalign{ & \Rightarrow \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} \cr & {\text{ = }}\frac{{100 - {\text{Discount}}\% }}{{100 + {\text{Profit}}\% }} \cr & {\text{ = }}\frac{{100 - 12}}{{100 + 32}} \cr & {\text{ = }}\left. {\frac{{88}}{{132}}} \right]{\text{ 44}} \cr & \therefore {\text{Required }}\% {\text{ }} \cr & = \frac{{44}}{{88}} \times 100 \cr & = 50\% \cr} $$

Cost price of shoes = Rs. 1200 Selling price of shoes =$${\text{ 1200}} \times \frac{{112}}{{100}}$$ Let Marked price of shoes = x Then, $$\eqalign{ & \Rightarrow x \times \frac{{84}}{{100}} \cr & = 1200 \times \frac{{112}}{{100}} \cr & = \frac{{1200 \times 112}}{{84}} \cr & = {\text{Rs}}{\text{. 1600}} \cr} $$

$$\eqalign{ & {\text{Single equivalent discount }} \cr & = \left( {20 + \frac{{25}}{4} - \frac{{20 \times 25}}{{400}}} \right)\% \cr & = 25\% \cr} $$ Let cost price of article = Rs. 100 ∴ Selling price of article = Rs. 120 (20% profit) Let the marked price of article = Rs. x $$\eqalign{ & \therefore x \times \frac{{75}}{{100}} = 120 \cr & \Rightarrow x = \frac{{120 \times 100}}{{75}} \cr & \Rightarrow x = {\text{Rs}}{\text{. 160}} \cr & {\text{Required percentage }} \cr & {\text{ = }}\frac{{160 - 100}}{{100}} \times 100 \cr & = 60\% \cr} $$

$$\eqalign{ & {\text{Selling price}} \cr & = 150 \times \frac{{80}}{{100}} \cr & = {\text{ Rs}}{\text{. 120 }} \cr} $$

$$\eqalign{ & {\text{Discount }} \cr & {\text{ = 6000}} - {\text{5500 }} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Discount}}\% {\text{ }} \cr & = \frac{{500}}{{6000}} \times 100 \cr & = \frac{{50}}{6} \cr & = \frac{{25}}{3}{\text{ }} \cr & = 8\frac{1}{3}\% \cr} $$

$${\text{Marked price}} \times \frac{{70}}{{100}}$$ $$ = {\text{Rs}}{\text{. 6580}}$$ $$\eqalign{ & {\text{Marked price}} = \frac{{6580 \times 100}}{{70}} \cr & {\text{Market Price}} = {\text{Rs}}{\text{. 9400 }} \cr} $$

$$\eqalign{ & {\text{Single equivalent discount}} \cr & = \left( {50 + 40 - \frac{{50 \times 40}}{{100}}} \right)\% \cr & = 70\% \cr & \therefore {\text{Required price of shirt }} \cr & {\text{ = }}\left( {100 - 70} \right)\% {\text{ of }}x \cr & = 30\% {\text{ of }}x \cr} $$

$$\eqalign{ & \therefore {\text{True discount is }} \cr & = \frac{{{\text{Banker's discount}} \times {\text{100}}}}{{100 + {\text{rate}} \times {\text{time}}}} \cr & = \frac{{216 \times 100}}{{100 + 16 \times \frac{6}{{12}}}} \cr & = \frac{{21600}}{{108}} \cr & = {\text{Rs}}{\text{. 200}} \cr} $$

Cost price of tape recorder = Rs. 1500 Marked price of tape recorder $$\eqalign{ & {\text{ = 120}}\% {\text{ of 1500}} \cr & = \frac{{120}}{{100}} \times 1500 \cr & {\text{ = Rs}}{\text{. }}1800 \cr} $$ Selling price of tape recorder $$\eqalign{ & {\text{ = 108}}\% {\text{ of 1500}} \cr & = \frac{{108}}{{100}} \times 1500 \cr & {\text{ = Rs}}{\text{. }}1620 \cr & {\text{Rate of discount }} \cr & = \frac{{1800 - 1620}}{{1800}} \times 100\% \cr & = \frac{{180}}{{1800}} \times 100 \cr & = 10\% \cr} $$

$$\eqalign{ & {\text{For same article}}, \cr & \frac{{100 - {d_1}}}{{100 - {d_2}}} = \frac{{100 + {g_1}}}{{100 + {g_2}}} \cr & \Rightarrow \frac{{100 - 25}}{{100 - 10}} = \frac{{100 + 25}}{{100 + {g_2}}} \cr & \Rightarrow \frac{{75}}{{90}} = \frac{{125}}{{100 + {g_2}}} \cr & \Rightarrow 100 + {g_2} = \frac{{90 \times 125}}{{75}} \cr & \Rightarrow 100 + {g_2} = 150 \cr & \therefore {g_2} = 50\% \cr} $$

$$\eqalign{ & {\text{Single discount = 50}}\% \cr & {\text{Two successive discount}} \cr & {\text{ = 40}} + {\text{10}} - \frac{{40 \times 10}}{{100}} \cr & = 50 - 4 \cr & = 46 \cr & {\text{Difference}} \cr & = 50 - 46 \cr & = 4\% \cr & {\text{Difference amount }} \cr & {\text{ = 4}}\% {\text{ of 10000}} \cr & {\text{ = }}\frac{4}{{100}} \times 10000 \cr & {\text{ = Rs}}{\text{. 400}} \cr} $$