Practice MCQ Questions and Answer on True Discount

121.

The price that akbar should marks on a pair of shoes which costs him Rs. 1200 to gain 12% after allowing a discount of 16% (in rupees) is = ?

• (A) Rs. 1344
• (B) Rs. 1433
• (C) Rs. 1600
• (D) Rs. 1500

Show Answer

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

122.

A shopkeeper marks the price of an item keeping 20% profit. If he offers a discount of $${\text{12}}\frac{1}{2}\% $$   on the marked price, his gain percent will be = ?

• (A) 4.5%
• (B) 5%
• (C) 7.5%
• (D) 8%

Show Answer

 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 $$\eqalign{ & \frac{{87.5}}{{100}} \times {\text{120 = Rs}}{\text{. 105}} \cr & {\text{Profit}}\% {\text{ }} = \frac{{105 - 100}}{{100}}{\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{ }}5\% {\text{ }} \cr} $$

123.

A shopkeeper sold an item for Rs. 1510 after giving a discount of $$24\frac{1}{2}\% $$   and there by incurred a loss of 10%. Had he sold the item without discount his net profit would have been = ?

• (A) Rs. 641
• (B) $${\text{Rs}}{\text{. 322}}\frac{1}{9}$$
• (C) $${\text{Rs}}{\text{. 422}}\frac{2}{9}$$
• (D) $${\text{Rs}}{\text{. 322}}\frac{2}{9}$$

Show Answer

 Let the marked price of an item = Rs. x Selling price of an item $$ = \left( {100 - 24\frac{1}{2}} \right)\% \,{\text{of }}x$$ $$\eqalign{ & \Rightarrow 1510 = \frac{{151}}{2} \times \frac{1}{{100}} \times x \cr & \Rightarrow x = {\text{Rs}}{\text{. 2000}} \cr & {\text{Cost price of an item }} \cr & = 1510 \times \frac{{100}}{{90}} \cr & {\text{ = Rs}}{\text{. }}\frac{{15100}}{9} \cr & {\text{Without discount, gain}} \cr & {\text{ = }}2000 - \frac{{15100}}{9} \cr & = \frac{{18000 - 15100}}{9} \cr & = \frac{{2900}}{9} \cr & = {\text{Rs}}{\text{. 322}}\frac{2}{9} \cr} $$

124.

To attract more visitors, zoo authority announces 20% discount on every ticket which cost 25 paise. For this reason, sale of ticket increase by 28%. Find the percentage of increase in the number of visitors ?

• (A) 40%
• (B) 50%
• (C) 60%
• (D) No change

Show Answer

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

125.

An article is marked 35% above cost. If a profit of 20% is earned by selling the article, then the discount percent offered on the marked price of the article is:

• (A) 12%
• (B) $$10\frac{1}{9}\% $$
• (C) $$11\frac{1}{9}\% $$
• (D) 15%

Show Answer

 Let cost price = 100 \[\begin{array}{*{20}{c}} {{\text{Cost price}}}&{}&{{\text{Selling price}}}&{}&{{\text{Marked price}}} \\ {100}&:&{120}&:&{135} \end{array}\] Discount % = $$\frac{{15}}{{135}}$$ × 100 = $$11\frac{1}{9}\% $$

126.

How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price ?

• (A) 50%
• (B) 40%
• (C) 60%
• (D) 45%

Show Answer

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

127.

Ramesh marks his goods 30% above cost price. If he sells the item for Rs. 910 afters allowing of 15% discount. Find his cost price ?

• (A) Rs. 823.5
• (B) Rs. 758
• (C) Rs. 814.2
• (D) Rs. 856.5

Show Answer

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

128.

A washing machine is sold at a discount of 30%. If a man buys it for Rs. 6580, its list price is = ?

• (A) Rs. 7500
• (B) Rs. 8600
• (C) Rs. 9400
• (D) Rs. 6990

Show Answer

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

129.

A merchant marks his goods 40% above the cost price and sell them at a discount of 15%. Find his gain % = ?

• (A) 25%
• (B) 22%
• (C) 19%
• (D) 20%

Show Answer

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

130.

A retailer purchases a grinder at a discount of 15% of the whole seller and sales it for Rs. 1955 at a profit of 15%. The amount of discount received by the retailer from the whole seller was = ?

• (A) Rs. 720
• (B) Rs. 290
• (C) Rs. 300
• (D) Rs. 330

Show Answer

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