Practice MCQ Questions and Answer on True Discount

31.

A dealer offers a cash discount of 20% and still makes a profit of 20%. If he further sells 8 articles at a rate of 6 articles, then how much percentage above the cost price does he mark on each article?

• (A) 87.5%
• (B) 100%
• (C) 77.5%
• (D) 112.5%

Show Answer

 $$\eqalign{ & \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} = \frac{{100 - {\text{Discount}}}}{{100 + {\text{Profit}}}} \cr & = \frac{{100 - 20}}{{100 + 20}} \cr & = \frac{{80}}{{120}} \cr} $$ \[\begin{array}{*{20}{c}} {{\text{Cost price}}}&{{\text{Marked price}}} \\ {\frac{{80}}{8} = 10}&{\frac{{120}}{6} = 20} \end{array}\] Above = 20 - 10 = 10 Above % = $$\frac{{10}}{{10}}$$ × 100 = 100%

32.

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%

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

33.

The difference between discount of 35% and two successive discount of 20% on a certain bill was 22, the amount of the bill is = ?

• (A) Rs. 200
• (B) Rs. 220
• (C) Rs. 1100
• (D) Rs. 2200

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 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 $$\eqalign{ & \therefore \frac{1}{{100}}x = 22 \cr & x = {\text{Rs}}{\text{. }}2200 \cr} $$

34.

If on a market price the difference of selling price with a discount of 30% and two successive discounts of 20% and 10% is 72, then the marked price ( in rupees ) is ?

• (A) Rs. 3600
• (B) Rs. 3000
• (C) Rs. 2500
• (D) Rs. 2400

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 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, $$\eqalign{ & \Rightarrow {\text{2}}\% {\text{ of }}x{\text{ = 72}} \cr & \Rightarrow \frac{2}{{100}} \times x = 72 \cr & \Rightarrow x = \frac{{72 \times 100}}{2} \cr & \Rightarrow x = {\text{Rs}}{\text{. 3600}} \cr} $$

35.

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

36.

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

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

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

37.

The difference between simple interest and the true discount on Rs. 2400 due 4 years hence at 5% per annum simple interest is -

• (A) Rs. 70
• (B) Rs. 30
• (C) Rs. 50
• (D) Rs. 80

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 $$\eqalign{ & {\text{Given}}\,{\text{A}} = 2400 \cr & {\text{R}} = 5\% \cr & {\text{T}} = 4{\text{year}} \cr & \therefore \,TD\, = \frac{{A \times R \times T}}{{100 + R \times T}} \cr & TD = \frac{{2400 \times 4 \times 5}}{{100 + 20}} \cr & TD = {\text{Rs}}{\text{. }}400 \cr & \therefore \,{\text{S}}{\text{.I}}{\text{.}} - {\text{TD}} = \frac{{TD \times R \times T}}{{100}} \cr & = \frac{{400 \times 5 \times 4}}{{100}} \cr & = {\text{Rs}}{\text{. 80}}{\text{}} \cr} $$

38.

A housewife saved Rs. 2.50 in buying a dress on sale. If she spent Rs. 25 for the dress, approximately how much percent she saved in the transaction ?

• (A) 8%
• (B) 9%
• (C) 10%
• (D) 11%

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

39.

A shopkeeper allows 18% discount on the marked price of an article and still makes a profit of 23%. If he gains Rs. 18.40 on the sale of the article, then what is the marked price of the article?

• (A) Rs. 120
• (B) Rs. 136
• (C) Rs. 146
• (D) Rs. 140

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40.

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 $$\eqalign{ & \therefore {\text{Discount}}\% \cr & = \frac{{100}}{{500}} \times 100 \cr & = 20\% \cr} $$