Practice MCQ Questions and Answer on True Discount

41.

A trader allows a trade discount of 20% and a cash discount of $${\text{ 6}}\frac{1}{4}\% $$   on the marked price of the goods and gets a net gain of 20% of the cost. By how much above the cost should the goods be marked for the sale = ?

• (A) 40%
• (B) 50%
• (C) 60%
• (D) 70%

Show Answer

 $$\eqalign{ & {\text{Single equivalent discount }} \cr & = \left( {20 + \frac{{25}}{4} - \frac{{20 \times 25}}{{400}}} \right)\% \cr & = 25\% \cr} $$ Let cost price of article = Rs. 100 ∴ Selling price of article = Rs. 120 (20% profit) Let the marked price of article = Rs. x $$\eqalign{ & \therefore x \times \frac{{75}}{{100}} = 120 \cr & \Rightarrow x = \frac{{120 \times 100}}{{75}} \cr & \Rightarrow x = {\text{Rs}}{\text{. 160}} \cr & {\text{Required percentage }} \cr & {\text{ = }}\frac{{160 - 100}}{{100}} \times 100 \cr & = 60\% \cr} $$

42.

A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. His gain percent is = ?

• (A) 5%
• (B) 4%
• (C) 2%
• (D) 1%

Show Answer

 Let the cost price = Rs. 100 $$\eqalign{ & {\text{Market price }} \cr & {\text{ = 120}}\% {\text{ of 100 }} \cr & {\text{ = Rs}}{\text{. 120}} \cr & {\text{Selling price }} \cr & {\text{ = 85}}\% {\text{ of 120 }} \cr & {\text{ = }}\frac{{85}}{{100}} \times {\text{120 }} \cr & {\text{ = Rs}}{\text{. 102}} \cr & {\text{Gain }}\% = \frac{{102 - 100}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\% \cr} $$

43.

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 : $$\eqalign{ & 150 \times \frac{{80}}{{100}} = 120{\text{ units}} \cr & {\text{120 units = Rs. 840}} \cr & {\text{1 units = 7}} \cr & {\text{100 units = Rs. 700}} \cr} $$

44.

The marked price of the a watch is Rs. 1600. The shopkeeper gives successive discount of 10% and x% to the customer. It the customer pays Rs. 1224 for the watch, the value of x is = ?

• (A) 5%
• (B) 10%
• (C) 15%
• (D) 20%

Show Answer

 Marked price of watch = Rs. 1600 After 1st discount of 10% $$\eqalign{ & {\text{ = 1600}} \times \frac{{90}}{{100}} \cr & {\text{ = Rs}}{\text{. 1440}} \cr} $$ Customer pays (final selling price) = Rs. 1224 $$\eqalign{ & \frac{x}{{100}} \times 1440 = \left( {1440 - 1224} \right) \cr & \frac{x}{{100}} \times 1440 = 216 \cr & x = \frac{{216 \times 100}}{{1440}} \cr & x = 15\% \cr} $$

45.

A single discount equivalent to three successive discount of 6%, 15% and 14% is:

• (A) 68.714%
• (B) 34.357%
• (C) 31.286%
• (D) 17.5%

Show Answer

 $$\eqalign{ & {\text{Discount }}\% = x + y - \frac{{xy}}{{100}} \cr & {\text{2 years}} \to {\text{discount }}\% \cr & = 6 + 15 - \frac{{6 \times 15}}{{100}} \cr & = 21 - 0.9 \cr & = 20.1\% \cr & {\text{3 years}} \to {\text{discount }}\% \cr & = 20.1 + 14 - \frac{{20.1 \times 14}}{{100}} \cr & = 34.1 - 2.814 \cr & = 31.286\% \cr} $$

46.

A shopkeeper gives two successive discounts on an article marked Rs. 450. The first discount given is 10 percent. If the customer pays Rs. 344.25 for the article, the second discount gives is = ?

• (A) 14%
• (B) 10%
• (C) 12%
• (D) 15%

Show Answer

 $$\eqalign{ & {\text{Marked price of an article}} \cr & = {\text{Rs}}{\text{. 450}} \cr & {\text{After 1st discount}} \cr & = {\text{450}} \times \frac{{90}}{{100}} \cr & = {\text{Rs}}{\text{. 405}} \cr & {\text{Cost price of an article}} \cr & = {\text{Rs}}{\text{. 344}}{\text{.25}} \cr & {\text{Difference}} \cr & = {\text{Rs}}{\text{. 405}} - 344.25\, \cr & = {\text{Rs}}{\text{. 60}}{\text{.75}} \cr & {\text{2nd discount}} \cr & = \frac{{60.75}}{{405}} \times 100 \cr & = 15\% \cr} $$

47.

A trader allows two successive discounts of 30% and 15% on selling an article. If he gets Rs. 476 for that article, find its marked price = ?

• (A) Rs. 700
• (B) Rs. 400
• (C) Rs. 900
• (D) Rs. 800

Show Answer

 $$\eqalign{ & {\text{Let, Marked price = Rs}}{\text{. }}x \cr & \therefore x \times \frac{{70}}{{100}} \times \frac{{85}}{{100}} = 476 \cr & \Rightarrow x = 476 \times \frac{{100}}{{70}} \times \frac{{100}}{{85}} \cr & \Rightarrow x = {\text{Rs}}{\text{. }}800 \cr} $$

48.

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

Show Answer

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

49.

Successive discount of p% and q% on the catalogue price of an article is equivalent to a single discount of = ?

• (A) $$\left( {p - q - \frac{{pq}}{{100}}} \right)\% $$
• (B) $$\left( {p + q - \frac{{pq}}{{100}}} \right)\% $$
• (C) $$\left( {p - q + \frac{{pq}}{{100}}} \right)\% $$
• (D) $$\left( {p + q + \frac{{pq}}{{100}}} \right)\% $$

Show Answer

 $$ = \left( {p - q + \frac{{pq}}{{100}}} \right)\% $$

50.

The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:

• (A) Rs. 1800
• (B) Rs. 1450
• (C) Rs. 1360
• (D) Rs. 6800

Show Answer

 $$\eqalign{ & {\text{Sum}} = \frac{{S.I.\, \times\, T.D.}}{{ {S.I.} - {T.D.} }} \cr & = \frac{{85 \times 80}}{{ {85 - 80} }} \cr & = Rs.\,1360 \cr} $$