Practice MCQ Questions and Answer on True Discount

51.

A man sells a bicycle at marked price which is 30% higher than the cost price. If he gives some discount and sells it at Rs. 150 less than the marked price, he would still gain 20%. What is the percentage of discount offered ?

• (A) 7.69%
• (B) 1.83%
• (C) 7.54%
• (D) 7.23%

Show Answer

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

52.

The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:

• (A) Rs. 1325
• (B) Rs. 1300
• (C) Rs. 1350
• (D) Rs. 1500

Show Answer

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

53.

The marked price of a T.V. is Rs. 16000. After two successive discounts it is sold for Rs. 11400. If the first discount is 5%, then the rate of second discount is = ?

• (A) 15%
• (B) 20%
• (C) 30%
• (D) 25%

Show Answer

 Marked price of T.V. = Rs. 16000 $$\eqalign{ & {\text{After 1st discount}} \cr & {\text{ = 95}}\% {\text{ of 16000}} \cr & {\text{ = }}\frac{{95}}{{100}} \times 16000 \cr & {\text{ = Rs}}{\text{. 15200}} \cr} $$ Selling price of T.V. = Rs. 11400 $$\eqalign{ & {\text{ So, the 2nd discount be}}\% \cr & = \frac{{15200 - 11400}}{{15200}} \times 100 \cr & = \frac{{3800}}{{15200}} \times 100 \cr & = 25\% \cr} $$

54.

A shopkeeper marks his goods 30% above his cost price but allows a discount of 10% at the time of sale. His gain is = ?

• (A) 21%
• (B) 20%
• (C) 18%
• (D) 17%

Show Answer

 Let the cost price of goods = Rs. 100 Mark price of goods = Rs. 130 (30% discount) Selling price of goods = 90% of 130 = Rs. 117 Gain = 117 - 100 = Rs. 17 $${\text{Gain}}\% = \frac{{17}}{{100}} \times 100 = 17\% $$

55.

A shopkeeper earns a profit of 10% after allowing a discount of 20% on the marked price. The cost price of the article whose marked price is Rs. 880, is = ?

• (A) Rs. 704
• (B) Rs. 640
• (C) Rs. 774
• (D) Rs. 680

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

56.

List price of an article at a showroom is Rs. 2000 and it is being sold at successive discount of 20% and 10%, its net selling price will be = ?

• (A) Rs. 1900
• (B) Rs. 1700
• (C) Rs. 1440
• (D) Rs. 1400

Show Answer

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

57.

Radha marks her goods 25% above the cost price. She sells 35% of goods at the marked price, 40% at 15% discount and the remaining at 20% discount. What is her overall percentage gain?

• (A) 12.75
• (B) 10
• (C) 11.75
• (D) 11.25

Show Answer

 \[\begin{array}{*{20}{c}} {{\text{Cost price}}}&{}&{{\text{Marked price}}} \\ {400}&:&{500} \\ {{\text{Number of goods}}}& \to &{35:40:25 = 7:8:5} \\ {}&{}&\begin{gathered} {\text{Selling price}} \hfill \\ \, \downarrow \hfill \\ \end{gathered} \\ {7 \times 500}& = &{3500} \\ {8 \times 425}& = &{2000} \\ {5 \times 400}& = &{2000} \\ {{\text{Total selling price}}}& = &{{\text{Rs}}{\text{. }}8900} \\ {{\text{Cost price}}}& = &{400\left( {7 + 8 + 5} \right)} \\ {}& = &{{\text{Rs}}{\text{. }}8000} \\ {{\text{Profit}}}& = &{{\text{Selling price}} - {\text{Cost price}}} \\ {}& = &{8900 - 8000 = 900} \\ {{\text{Profit}}\,\% }&{ = \frac{{900}}{{8000}} \times 100}&{ = 11.25\% } \end{array}\]

58.

A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?

• (A) Rs. 9025.20
• (B) Rs. 9200
• (C) Rs. 9600
• (D) Rs. 9560

Show Answer

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

59.

A shopkeeper sells a badminton racket whose marked price is Rs. 30, at a discount of 15% and gives a shuttle cock costing Rs. 1.50 free with each racket. Even then he makes a profit of 20%. His cost price, per racket is = ?

• (A) Rs. 21.00
• (B) Rs. 21.25
• (C) Rs. 20.00
• (D) Rs. 17.75

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

60.

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