Practice MCQ Questions and Answer on True Discount

1.

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 $$\eqalign{ & {\text{ = }}\frac{{387 \times 100}}{{86}} \cr & = {\text{Rs}}{\text{. 450}} \cr} $$

2.

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

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

3.

A dealer buys an article marked at Rs. 25000 with 20% and 5% off. He spends Rs. 1000 for its repair and sells it for Rs. 25000 what is his gain or loss percent ?

• (A) Loss of 25%
• (B) Gain of 25%
• (C) Gain of 10%
• (D) Loss of 10%

Show Answer

 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 $$\eqalign{ & {\text{Gain}}\% \Rightarrow \frac{{25000 - 20000}}{{20000}} \times 100 \cr & {\text{Gain}}\% \Rightarrow \frac{1}{4} \times 100 \cr & {\text{Gain}}\% \Rightarrow 25\% \cr} $$

4.

The discount series 10%, 20%, 40% is equivalent to a single discount of = ?

• (A) 50%
• (B) 56.8%
• (C) 60%
• (D) 62.28%

Show Answer

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

5.

Discount on a pair of shoes marked at Rs. 475 and discounted at 15% is = ?

• (A) Rs. 70
• (B) Rs. 72
• (C) Rs. 71.25
• (D) Rs. 75.25

Show Answer

 Market price of shoes = Rs. 475 $$\eqalign{ & {\text{Discount}} = \frac{{15}}{{100}} \times 475 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{285}}{4}{\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs 71}}{\text{.25}} \cr} $$

6.

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

7.

A shopkeeper marks an article at such a price that after giving a discount of $$12\frac{1}{2}\% $$  on the marked price, he still earns a profit of 15%. If the cost price of the article is Rs. 385, then the sum of the marked price and the selling price (in Rs.) of the article is:

• (A) 948.75
• (B) 849.50
• (C) 954.75
• (D) 984.75

Show Answer

 $$\eqalign{ & 15\% = \frac{{15}}{{100}} = \frac{3}{{20}} \cr & 12\frac{1}{2}\% = \frac{1}{8} \cr} $$ \[\begin{array}{*{20}{c}} {{\text{Cost price }}\,\,{\text{ Selling price}}\,\,{\text{ Marked price}}} \\ {{{20}_{ \times 7}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{23}_{ \times 7}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{7_{ \times 23}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{8_{ \times 23}}} \\ {\overline {\,\,\,140\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,161\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,184\,\,\,\,\,\,\,} } \end{array}\] 140 units = 385 1 unit = $$\frac{{385}}{{140}}$$ Sum of the marked price and the selling price = 184 + 161 = 345 units 345 units = $$\frac{{385}}{{140}}$$ × 345 = 948.75

8.

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

9.

In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit percent of = ?

• (A) 30%
• (B) 32%
• (C) 33%
• (D) 35%

Show Answer

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

10.

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