Practice MCQ Questions and Answer on True Discount

21.

An article of cost price Rs. 8000 is marked at Rs. 11200, after allowing a discount of x percent a profit of 12% is made. The value of x is = ?

• (A) 21%
• (B) 20%
• (C) 22%
• (D) 23%

Show Answer

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

22.

Maha Bazaar offers 20% discount on bags which have been marked 50% above the cost price. Amarnath pays Rs. 840 for a bag. Then the cost price of the bag is = ?

• (A) Rs. 672
• (B) Rs. 700
• (C) Rs. 790
• (D) Rs. 810

Show Answer

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

23.

A discount of 14% on the marked price of an article is allowed and then the article is sold for Rs. 387. The marked price of the article is = ?

• (A) Rs. 450
• (B) Rs. 427
• (C) Rs. 500
• (D) Rs. 440

Show Answer

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

24.

A fan is listed at Rs. 150 and a discount of 20% is given. Then the selling price is = ?

• (A) Rs. 180
• (B) Rs. 150
• (C) Rs. 120
• (D) Rs. 110

Show Answer

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

25.

A single discount equivalent to the successive discounts of 10%, 20% and 25% is = ?

• (A) 55%
• (B) 45%
• (C) 46%
• (D) 60%

Show Answer

 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% $$\eqalign{ & = 28 + 25 - \frac{{28 \times 25}}{{100}} \cr & = 46\% \cr} $$

26.

A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?

• (A) Rs. 12,000 in cash
• (B) Rs. 12,880 at credit
• (C) Both are equally good
• (D) Rs. 18.33

Show Answer

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

27.

A store has an offer 'Buy 4 Get 1 Free'. What is the net percentage of discount ?

• (A) 25%
• (B) 33.3%
• (C) 20%
• (D) Insufficient Data

Show Answer

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

28.

A person paid Rs. 17000 for a motor-car after a single discount of 15%. If he is given successive discount of 5% and 10% then how much he would pay ?

• (A) Rs. 17000
• (B) Rs. 17010
• (C) Rs. 17100
• (D) Rs. 18900

Show Answer

 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 $$\eqalign{ & = {\text{Rs}}{\text{. 20000}} \times \frac{{95}}{{100}} \times \frac{{90}}{{100}} \cr & = {\text{Rs}}{\text{. 17100 }} \cr} $$

29.

A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any ?

• (A) 1% gain
• (B) 1% loss
• (C) 5% gain
• (D) No gain no loss

Show Answer

 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 : $$\eqalign{ & {\text{Loss}}\% {\text{ = }}\frac{{x \times y}}{{100}}\% \cr & {\text{Loss}}\% {\text{ = }}\frac{{10 \times 10}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% \cr} $$

30.

The true discount on a certain of money due $$\text{2}\frac{\text{2}}{\text{3}}$$ years hence, is Rs. 150 and the simple interest on the same sum for the same time and at the same rate is Rs. 200. Interest rate per annum is ?

• (A) 10%
• (B) 12%
• (C) $$\text{12}\frac{1}{2}\mathrm{\%}$$
• (D) $$\text{8}\frac{1}{2}\mathrm{\%}$$

Show Answer

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