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Home > Practice > Arithmetic Aptitude > True Discount > Miscellaneous

61. 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

Discuss

Solution:

Let the cost price of bag is = 100 units
∴ Marked price of the bag = 150 units
Selling price of the bag :

\begin{aligned} 150 \times \frac{80}{100} = 120 units \\ 120 units  =  Rs. 840 \\ 1 units  =  7 \\ 100 units  =  Rs. 700 \end{aligned}

62. An article of cost price Rs. 8000 is marked at Rs. 11200, after allowing a discount of x percent a profit of 12% is made. The value of x is = ?

A. 21%

B. 20%

C. 22%

D. 23%

Discuss

Solution:

Cost price of the article = Rs. 8000
Profit% = 12%
Selling price of the article

\begin{aligned} =  Cost price \times \frac{100 + P %}{100} \\ = 8000 \times \frac{112}{100} \\ =  Rs . 8960 \end{aligned}

\begin{aligned} ∴ Discount \\ =  Marked price - Selling price \\ = 11200 - 8960 \\ =  Rs . 2240 \end{aligned}

Let the discount percentage = x%

\begin{aligned} ∴ \frac{11200 \times x}{100} = 2240 \\ \Rightarrow x = \frac{2240 \times 100}{11200} \\ \Rightarrow x = 20 % \end{aligned}

Alternate :

\begin{aligned} \frac{100 - D %}{100 + P %} = \frac{Cost price}{Marked price} \\ \Rightarrow \frac{100 - x}{100 + 12} = \frac{5}{7} \\ \Rightarrow \frac{100 - x}{112} = \frac{5}{7} \\ \Rightarrow 700 - 7 x = 560 \\ \Rightarrow 7 x = 700 - 560 \\ \Rightarrow x = \frac{140}{7} \\ \Rightarrow x = 20 % \end{aligned}

63. While selling a watch, a shopkeeper gives a discount of 5%. If he gives a discount of 6%, he earns Rs. 15 less as profit, what is the marked price of the watch = ?

A. Rs. 1250

B. Rs. 1400

C. Rs. 1500

D. Rs. 750

Discuss

Solution:

Let the marked price = 100x
Shop Keeper gives 5% discount, therefore, Price becomes = 95x
Again if shopkeeper gives 6% discount then the price become = 94x
According to the question if he gives 6% discount his earning will Rs.15 less
∴ 95x - 94x = 15
⇒ x = 15
∴ Marked price = 100 × 15 = Rs. 1500

64. The price of shirt is Rs. 440 and a customer pays Rs. 396 for it. The discount rate is ?

A. 10%

B. $10 \frac{1}{2} %$

C. 20%

D. 12%

Discuss

Solution:

\begin{aligned} Discount % \\ = \frac{440 - 396}{440} \times 100 \\ = 10 % \end{aligned}

65. 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

Discuss

Solution:

\begin{aligned} Let, Marked price  =  Rs . x \\ ∴ x \times \frac{70}{100} \times \frac{85}{100} = 476 \\ \Rightarrow x = 476 \times \frac{100}{70} \times \frac{100}{85} \\ \Rightarrow x = Rs . 800 \end{aligned}

66. The true discount on a certain of money due $2 \frac{2}{3}$ years hence, is Rs. 150 and the simple interest on the same sum for the same time and at the same rate is Rs. 200. Interest rate per annum is ?

A. 10%

B. 12%

C. $12 \frac{1}{2} %$

D. $8 \frac{1}{2} %$

Discuss

Solution:

\begin{aligned} True Discount = Rs . 150 \\ and \\ Simple interest = Rs . 200 \\ Sum due = \frac{S .I . \times TD}{(S .I .) - (TD)} \\ = Rs . (\frac{200 \times 150}{200 - 150}) \\ = Rs . 600 \\ ∴ Rate \\ = (\frac{100 \times 200}{600 \times \frac{8}{3}}) % \\ = (\frac{20000}{1600}) % \\ = (\frac{200}{16}) % \\ = 12 \frac{1}{2} % \end{aligned}

67. The marked price of a table is Rs. 800. A retailer bought it after two successive discounts of 10% and 15%. He spent Rs. 13 on transportation and sold it for Rs. 875. His profit was = ?

A. 40%

B. 37%

C. 28%

D. 25%

Discuss

Solution:

\begin{aligned} Cost price for the retailer \\ = 800 \times \frac{90}{100} \times \frac{85}{100} + 13 \\ = 612 + 13 \\ =  Rs. 625 \\ Selling price  =  Rs . 875 \\ ∴ Profit % \\ = \frac{875 - 625}{625} \times 100 \\ = \frac{250}{625} \times 100 \\ = 40 % \end{aligned}

68. 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

Discuss

Solution:

Let the number of visitors in the beginning = 100

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

69. 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%

Discuss

Solution:

Let the cost price = 100 units
Marked price = 140 units
Selling price = 140 ×

\frac{85}{100}

= 119

\begin{aligned} Profit % = \frac{19}{100} \times 100 \\ = 19 % \end{aligned}

70. The marked price is 20% higher then cost price. A discount of 20% is given on the marked price. By this type of sale, there is = ?

A. 4% loss

B. 2% loss

C. No loss no gain

D. 4% gain

Discuss

Solution:

Let the cost price = 100 units
Marked price = 120 units
Selling price = 120 ×

\frac{80}{100}

= 96 units
There will be loss

\begin{aligned} Loss % = \frac{100 - 96}{100} \times 100 \\ = 4 % \end{aligned}

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