True Discount — Part 1 MCQs with Explanations

$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = Rs.\,3000 \cr & {\text{S}}{\text{.P}}{\text{.}} = Rs.\,\left[ {\frac{{3600 \times 100}}{{100 + \left( {10 \times 2} \right)}}} \right] \cr & = Rs.\,3000 \cr & {\text{Gain}} = 0\% \cr} $$

$$\eqalign{ & {\text{P}}{\text{.W}}{\text{.}} = Rs.\left( {2562 - 122} \right) \cr & = Rs.2440 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{2440}}\,{\text{for}}\,{\text{4}}\,{\text{months}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{122}}{\text{.}} \cr & \therefore {\text{Rate}} = \left[ {\frac{{100 \times 122}}{{2440 \times \frac{1}{3}}}} \right]\% = 15\% \cr} $$

$$\eqalign{ & {\text{Required}}\,{\text{Money}} \cr & {\text{ = }}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{10028}}\,{\text{due}}\,{\text{9}}\,{\text{months}}\,{\text{hence}} \cr & = Rs.\,\left[ {\frac{{10028 \times 100}}{{100 + \left( {12 \times \frac{9}{{12}}} \right)}}} \right] \cr & = Rs.\,9200 \cr} $$

$$\eqalign{ & {\text{ = }}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{12,880}}\,{\text{due}}\,{\text{8}}\,{\text{months}}\,{\text{hence}} \cr & = Rs.\,\left[ {\frac{{12880 \times 100}}{{100 + \left( {18 \times \frac{8}{{12}}} \right)}}} \right] \cr & = Rs.\,\left( {\frac{{12880 \times 100}}{{112}}} \right) \cr & = Rs.\,11500 \cr} $$ Clearly 12000 in cash is a better offer.

S.I. on Rs. (110 - 10) for a certain time = Rs. 10. S.I. on Rs. 100 for double the time = Rs. 20. T.D. on Rs. 120 = Rs. (120 - 100) = Rs. 20. $$\eqalign{ & {\text{T}}{\text{.D}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{110}} \cr & = Rs.\,\left( {\frac{{20}}{{120}} \times 110} \right) \cr & = Rs.\,18.33 \cr} $$

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = 102\% \,of\,Rs.\,600 \cr & = {\frac{{102}}{{100}} \times 600} \cr & = Rs.\,612 \cr & {\text{Now,}}\,\cr & {\text{P}}{\text{.W}}{\text{. = Rs}}{\text{. 612}}\,{\text{and}}\,{\text{sum}} = Rs.\,688.50 \cr & \therefore {\text{T}}{\text{.D}}{\text{.}} = Rs.\,\left( {688.50 - 612} \right) \cr & = Rs.\,76.50. \cr & {\text{Thus,}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{612}}\,{\text{for}}\,{\text{9}}\,{\text{months}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{76}}{\text{.50}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 76.50}}{{612 \times \frac{3}{4}}}} \right)\% \cr & = 16\frac{2}{3}\% \, \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{x}}{\text{.}} \cr & {\text{Then,}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{x}}\,{\text{at}}\,{\text{16}}\% \,{\text{for}}\,{\text{9}}\,{\text{months}} \cr & = Rs.\,189 \cr & \therefore x \times 16 \times \frac{9}{{12}} \times \frac{1}{{100}} \cr & = 189\,or\,x = 1575. \cr & \therefore P.W. = Rs.\,1575. \cr & \therefore {\text{Sum}}\,{\text{due}} = P.W. + T.D. \cr & = Rs.\left( {1575 + 189} \right) \cr & = Rs.\,1764 \cr} $$

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. = P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{2200}}\,{\text{due}}\,{\text{1}}\,{\text{year}}\,{\text{hence}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left[ {\frac{{2200 \times 100}}{{100 + \left( {10 \times 1} \right)}}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,2000 \cr & \therefore {\text{Gain}} = Rs.\left( {2000 - 1950} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,50 \cr} $$

$$\eqalign{ & P.W. = Rs.\left( {1760 - 160} \right) = Rs.\,1600 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{12}}\% \,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{160}}{\text{}} \cr & \therefore {\text{Time}} = {\frac{{100 \times 160}}{{1600 \times 12}}} \cr & = \frac{5}{6}{\text{years}} \cr & = \left( {\frac{5}{6} \times 12} \right){\text{months}} \cr & = 10\,{\text{months}}{\text{}} \cr} $$

$$\eqalign{ & P.W. = Rs.\,\left[ {\frac{{100 \times 2310}}{{100 + \left( {15 \times \frac{5}{2}} \right)}}} \right] \cr & = Rs.\,1680 \cr} $$

S.I. on Rs. (260 - 20) for a given time = Rs. 20 S.I. on Rs. 240 for half time = Rs. 10 T.D. on Rs. 250 = Rs. 10 ∴ T.D. on Rs. 260 = Rs. $$\frac{10}{250}$$ × 260 = Rs. 10.40

S.I. on Rs. 750 = T.D. on Rs. 960 This means P.W. of Rs. 960 due 2 years hence is Rs. 750 ∴ T.D. = Rs. (960 - 750) = Rs. 210 Thus, S.I. on R.s 750 for 2 years is Rs. 210 $$\eqalign{ & \therefore {\text{Rate}} = \left( {\frac{{100 \times 210}}{{750 \times 2}}} \right)\% \cr & = 14\% \cr} $$

$$\eqalign{ & {\text{Sum}} = \frac{{S.I.\, \times\, T.D.}}{{ {S.I.} - {T.D.} }} \cr & = \frac{{85 \times 80}}{{ {85 - 80} }} \cr & = Rs.\,1360 \cr} $$

Required sum = P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence $$\eqalign{ & = Rs.\,\left[ { {\frac{{100 \times 702}}{{100 + 8 \times \frac{1}{2}}}} + {\frac{{100 \times 702}}{{100 + \left( {8 \times 1} \right)}}} } \right] \cr & = Rs.\,\left( {675 + 650} \right) \cr & = Rs.\,1325 \cr} $$

$$\eqalign{ & P.W. = \frac{{100 \times T.D.}}{{R \times T}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100 \times 168}}{{14 \times 2}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 600 \cr & \therefore {\text{Sum}} = \left( {P.W. + T.D.} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\left( {600 + 168} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,768 \cr} $$

Let cost price of goods = Rs 100 Market price of goods $$\eqalign{ & = 110\% {\text{ of }}100{\text{ }} \cr & = \frac{{110}}{{100}} \times 100 \cr & {\text{ = Rs}}{\text{. 110}} \cr} $$ After discount selling price of goods $$\eqalign{ & = 90\% {\text{ of }}110 \cr & = \frac{{90}}{{100}} \times 110 \cr & = {\text{Rs}}{\text{. 99}} \cr} $$ Loss = 100 - 99 = Rs. 1 $$\eqalign{ & {\text{Loss }}\% {\text{ = }}\frac{1}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% \cr} $$ Alternate : $$\eqalign{ & {\text{Loss}}\% {\text{ = }}\frac{{x \times y}}{{100}}\% \cr & {\text{Loss}}\% {\text{ = }}\frac{{10 \times 10}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% \cr} $$

Discount = 2.5% \[ = \frac{{2.5}}{{100}} = \frac{1}{{40}}\begin{array}{*{20}{c}} { \to {\text{Discount}}} \\ {{\text{ }} \to {\text{Market Price}}} \end{array}\] Market Price = Rs. 40 Discount = Rs. 1 Cost Price = 40 - 1 = Rs. 39 39 → 39 Actual Cost Price 40 → Rs. 40

Market price of a watch = Rs. 720 After 1 st discount $$\eqalign{ & {\text{ = 90}}\% {\text{ of 720 }} \cr & {\text{ = }}\frac{{90}}{{100}} \times 720 \cr & = {\text{Rs}}{\text{. 648}} \cr} $$ Cost price of watch = Rs. 550.80 Difference = 648 - 550.80 = Rs. 97.20 $$\eqalign{ & {{\text{2}}^{{\text{nd}}}}{\text{ discount}} \cr & = \frac{{97.20}}{{648}} \times 100 \cr & = \frac{{9720}}{{648}} \cr & = 15\% \cr} $$

Let the cost price of goods = Rs. 100 Market price of goods $$\eqalign{ & {\text{ = 120}}\% {\text{ of 100 }} \cr & {\text{ = }}\frac{{120}}{{100}} \times {\text{100}} \cr & {\text{ = Rs}}{\text{. 120}} \cr} $$ After discount selling price of goods = 70% of 120 = Rs. 84 $$\eqalign{ & {\text{Loss = 100}} - 84 = {\text{Rs}}{\text{.16}} \cr & {\text{Loss }}\% {\text{ = }}\frac{{16}}{{100}} \times 100 = 16\% \cr} $$ Alternate : $$\eqalign{ & {\text{Formula = }}x \pm y \pm {\text{ }}\frac{{x \times y}}{{100}} \cr & {\text{Loss}}\% {\text{ = 20}} - {\text{30}} - \frac{{20 \times 30}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 10 - 6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 16\% {\text{ }}({\text{Loss)}} \cr} $$

Equivalent to a single discount $$\eqalign{ & = 15 + 10 - \frac{{15 \times 10}}{{100}} \cr & = 25 - 1.5 \cr & = 23.5\% \cr} $$ Alternate : $$\eqalign{ & {\text{Market price = Rs}}{\text{.100}} \cr & {\text{Cost price}} \cr & {\text{ = 100}} \times \frac{{85}}{{100}} \times \frac{{90}}{{100}} \cr & {\text{ = Rs}}{\text{. }}76.5 \cr & {\text{Difference = 100}} - 76.5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23.5 \cr & {\text{Difference}}\% \cr & = \frac{{23.5}}{{100}} \times 100 \cr & = 23.5\% \cr} $$

Market price of the article = Rs. 880 After discount selling price of the article $$\eqalign{ & {\text{ = }}\frac{{880 \times 80}}{{100}} \cr & {\text{ = Rs}}{\text{. 704}} \cr & {\text{Cost price of the article }} \cr & {\text{ = }}\frac{{704 \times 100}}{{110}} \cr & = {\text{Rs}}{\text{. 640}} \cr} $$

Listed price of fan = Rs. 1500 After discount listed price $$\eqalign{ & {\text{ = 80}}\% {\text{ of 1500}} \cr & {\text{ = }}\frac{{80}}{{100}} \times {\text{1500 }} \cr & {\text{ = Rs}}{\text{. 1200}} \cr} $$ Net price of fan = Rs. 1104 Differece = 1200 - 1104 = Rs. 96 Additional discount $$\eqalign{ & {\text{ = }}\frac{{96}}{{1200}} \times 100 \cr & = 8\% \cr} $$

Let the price is = Rs. 100 After discount price $$\eqalign{ & {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{80}}{{100}} \times \frac{{75}}{{100}} \cr & {\text{ = Rs}}{\text{. 54}} \cr & {\text{Difference = 100}} - 54 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 46\% \cr} $$ So, 46% 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 25% $$\eqalign{ & = 28 + 25 - \frac{{28 \times 25}}{{100}} \cr & = 46\% \cr} $$

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% $$\eqalign{ & = 28 + 40 - \frac{{28 \times 40}}{{100}} \cr & = 56.8\% \cr} $$

Let the cost price of an article = Rs. 100 Marked price of an article = Rs. 110 (10% above) Selling price of an article = Rs. 99 (10% discount) $$\eqalign{ & {\text{Difference}} = {\text{ }}110 - 99{\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 11}} \cr & {\text{Discount}} = \frac{{11}}{{110}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$

Selling price of article = Rs. 387 Mark price of article $$\eqalign{ & {\text{ = }}\frac{{387 \times 100}}{{86}} \cr & = {\text{Rs}}{\text{. 450}} \cr} $$

Mark price of scooter = Rs. 36000 According to question, $${\text{20000}} \times \frac{8}{{100}} + $$ $$10000 \times \frac{5}{{100}}{\text{ + }}$$ $${\text{ 6000}} \times \frac{x}{{100}}$$ $$ = {\text{36000}} \times \frac{7}{{100}}$$ $$\eqalign{ & \Rightarrow 1600 + 500 + 60x = 2520 \cr & \Rightarrow 60x = 420 \cr & \Rightarrow x = \frac{{420}}{{60}} \cr & \Rightarrow x = 7\% \cr} $$

House wife spends Rs. 25 on dress and saved Rs. 2.50 Total transaction = 25 + 2.50 = Rs. 27.50 $$\eqalign{ & {\text{Save }}\% = \frac{{2.50}}{{27.50}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{{11}}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 9\% {\text{ ( approx)}} \cr} $$

List price of an article = Rs. 2000 After discount, selling price $$\eqalign{ & = {\text{2000}} \times \frac{{80}}{{100}} \times \frac{{90}}{{100}} \cr & {\text{ = Rs}}{\text{. 1440}} \cr} $$

Let the cost price of goods = Rs. 100 Selling price of goods = 120% of 100 = Rs. 120 Mark price of goods $$\eqalign{ & {\text{ = 120}} \times \frac{{100}}{{90}} \cr & = \frac{{400}}{3}{\text{ }} \cr} $$ Difference of Mark price and Cost price $$\eqalign{ & {\text{ = }}\frac{{400}}{3} - 100 \cr & {\text{Difference }}\% \cr & = \frac{{\frac{{100}}{3}}}{{100}} \times 100 \cr & = \frac{{100}}{3}\% \cr & = 33\frac{1}{3}\% \cr} $$

CP SP MP 100 ×10 117 ×10 90 ×13 100 ×13 1000 1170 1300 $$\eqalign{ & \therefore {\text{L}}{\text{.C}}{\text{.M of 117 and 90}} \cr & {\text{Profit}} = {\text{1300}} - {\text{1000}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 300}} \cr & {\text{Profit}} = \frac{{300}}{{1000}} \times {\text{100 }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{30% }} \cr} $$

Mark price of racket = Rs. 30 After discount selling price = 85% of Rs. 30 $$\eqalign{ & = \frac{{85}}{{100}} \times 30{\text{ }} \cr & = {\text{Rs}}{\text{. 25}}{\text{.50 }} \cr & {\text{Selling price of racket }} \cr & = {\text{25}}{\text{.50}} - {\text{1}}{\text{.50}} \cr & = {\text{Rs}}{\text{. 24}} \cr & {\text{Cost price of racket}} \cr & = 24 \times \frac{{100}}{{120}}{\text{ }} \cr & = {\text{Rs}}{\text{. 20}} \cr} $$

Cost price of motor-car = Rs. 17000 Mark price of motor-car $$\eqalign{ & = {\text{Rs}}{\text{. 17000}} \times \frac{{100}}{{85}}{\text{ }} \cr & = {\text{Rs}}{\text{. 20000}} \cr} $$ After successive discount,Cost price $$\eqalign{ & = {\text{Rs}}{\text{. 20000}} \times \frac{{95}}{{100}} \times \frac{{90}}{{100}} \cr & = {\text{Rs}}{\text{. 17100 }} \cr} $$

Let, Marked price of the thing is Rs. 100 SP Discount MP 400 100 500 $$\eqalign{ & \therefore {\text{Discount}}\% \cr & = \frac{{100}}{{500}} \times 100 \cr & = 20\% \cr} $$

$$\eqalign{ & {\text{Marked price of article }} \cr & = {\text{Rs}}{\text{. 500}} \cr & {\text{Selling price of article }} \cr & = {\text{90% }}\,{\text{of}}\,{\text{500}} \cr & = \frac{{90}}{{100}} \times 500{\text{ }} \cr & = {\text{Rs}}{\text{. 450}} \cr & {\text{Cost price of article }} \cr & = 450 \times \frac{{100}}{{120}}{\text{ }} \cr & = {\text{Rs}}{\text{. 375}} \cr} $$

$$\eqalign{ & {\text{Marked price of an article}} \cr & = {\text{Rs}}{\text{. 450}} \cr & {\text{After 1st discount}} \cr & = {\text{450}} \times \frac{{90}}{{100}} \cr & = {\text{Rs}}{\text{. 405}} \cr & {\text{Cost price of an article}} \cr & = {\text{Rs}}{\text{. 344}}{\text{.25}} \cr & {\text{Difference}} \cr & = {\text{Rs}}{\text{. 405}} - 344.25\, \cr & = {\text{Rs}}{\text{. 60}}{\text{.75}} \cr & {\text{2nd discount}} \cr & = \frac{{60.75}}{{405}} \times 100 \cr & = 15\% \cr} $$

\[\begin{gathered} {\text{30}}\% = \frac{{{3^{{ \nearrow ^{{\text{gain}}}}}}}}{{{\text{ }}{{10}_{{ \searrow _{{\text{cost price}}}}}}}}{\text{marked price}} = 13{\text{ }} \hfill \\ {\text{20}}\% = \frac{{{1^{{ \nearrow ^{{\text{profit}}}}}}}}{{{\text{ }}{5_{{ \searrow _{{\text{cost price}}}}}}}}{\text{selling price}} = 6{\text{ }} \hfill \\ \end{gathered} \] \[\begin{gathered} \begin{array}{*{20}{c}} {{\text{Cost price}}}&{{\text{Selling price}}}&{{\text{Marked price}}} \\ {10}&{}&{13} \\ {5 \times 2}&{6 \times 2}&{} \end{array} \hfill \\ {\text{ }}\overline {\,\,\,10{\text{ units}}\,\,\,\,\,\,\,\,\,\,\,\underbrace {12\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1{\text{3 unit}}}_{{\text{discount = 1}}}} \hfill \\ \end{gathered} \] $$\eqalign{ & \therefore {\text{Discount }}\% \cr & = \frac{1}{{13}} \times 100 \cr & = 7.69\% \cr} $$

Selling price of an article = Rs. 660 $$\eqalign{ & {\text{Cost price of an article}} \cr & = 660 \times \frac{{100}}{{110}} \cr & = {\text{Rs}}{\text{. 600}} \cr & {\text{Marked price of an article}} \cr & = 600 \times \frac{{100}}{{75}} \cr & = {\text{Rs}}{\text{. 800}} \cr} $$

Marked price of an article = Rs. 25000 After discount, cost price $$ = {\text{Rs}}{\text{. 25000}} \times \frac{{80}}{{100}} \times \frac{{95}}{{100}}$$ = Rs. 19000 After repair, cost price = Rs. 19000 + 1000 = Rs. 20000 Selling price of an article = Rs. 25000 $$\eqalign{ & {\text{Gain}}\% \Rightarrow \frac{{25000 - 20000}}{{20000}} \times 100 \cr & {\text{Gain}}\% \Rightarrow \frac{1}{4} \times 100 \cr & {\text{Gain}}\% \Rightarrow 25\% \cr} $$

Marked price of the article = Rs. x According to the question, $$⇒$$ 80% of 70% of x = 2240 $$\eqalign{ & \Rightarrow \frac{{80}}{{100}} \times \frac{{70}}{{100}} \times x = 2240 \cr & \Rightarrow x = {\text{Rs}}{\text{. 4000}} \cr} $$