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71. How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price ?

A. 50%

B. 40%

C. 60%

D. 45%

Discuss

Solution:

\begin{aligned} \Rightarrow \frac{Cost price}{Marked price} \\ = \frac{100 - Discount %}{100 + Profit %} \\ = \frac{100 - 12}{100 + 32} \\ = \frac{88}{132}] 44 \\ ∴ Required % \\ = \frac{44}{88} \times 100 \\ = 50 % \end{aligned}

72. The price that akbar should marks on a pair of shoes which costs him Rs. 1200 to gain 12% after allowing a discount of 16% (in rupees) is = ?

A. Rs. 1344

B. Rs. 1433

C. Rs. 1600

D. Rs. 1500

Discuss

Solution:

Cost price of shoes = Rs. 1200
Selling price of shoes =

1200 \times \frac{112}{100}

Let Marked price of shoes = x
Then,

\begin{aligned} \Rightarrow x \times \frac{84}{100} \\ = 1200 \times \frac{112}{100} \\ = \frac{1200 \times 112}{84} \\ = Rs . 1600 \end{aligned}

73. A trader allows a trade discount of 20% and a cash discount of $6 \frac{1}{4} %$ 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%

Discuss

Solution:

\begin{aligned} Single equivalent discount \\ = (20 + \frac{25}{4} - \frac{20 \times 25}{400}) % \\ = 25 % \end{aligned}

Let cost price of article = Rs. 100
∴ Selling price of article = Rs. 120 (20% profit)
Let the marked price of article = Rs. x

\begin{aligned} ∴ x \times \frac{75}{100} = 120 \\ \Rightarrow x = \frac{120 \times 100}{75} \\ \Rightarrow x = Rs . 160 \\ Required percentage \\ = \frac{160 - 100}{100} \times 100 \\ = 60 % \end{aligned}

74. A fan is listed at Rs. 150 and a discount of 20% is given. Then the selling price is = ?

A. Rs. 180

B. Rs. 150

C. Rs. 120

D. Rs. 110

Discuss

Solution:

\begin{aligned} Selling price \\ = 150 \times \frac{80}{100} \\ = Rs . 120 \end{aligned}

75. If a table marked price Rs. 6000 was sold to a customer for Rs. 5500, then the rate of discount allowed on the table is = ?

A. 10%

B. 8%

C. $8 \frac{1}{3} %$

D. 9%

Discuss

Solution:

\begin{aligned} Discount \\ =  6000 - 5500 \\ =  Rs . 500 \\ Discount % \\ = \frac{500}{6000} \times 100 \\ = \frac{50}{6} \\ = \frac{25}{3} \\ = 8 \frac{1}{3} % \end{aligned}

76. A washing machine is sold at a discount of 30%. If a man buys it for Rs. 6580, its list price is = ?

A. Rs. 7500

B. Rs. 8600

C. Rs. 9400

D. Rs. 6990

Discuss

Solution:

Marked price \times \frac{70}{100}

= Rs . 6580

\begin{aligned} Marked price = \frac{6580 \times 100}{70} \\ Market Price = Rs . 9400 \end{aligned}

77. During month-long annual sale, a shopkeeper sells his goods at a discount of 50%. But in the last week, he offers an additional discount of 40%. If the original price of a shirt is Rs. x, then the price (in rupees) during the last week of the sale will be = ?

A. 90% of x

B. 70% of x

C. 30% of x

D. 10% of x

Discuss

Solution:

\begin{aligned} Single equivalent discount \\ = (50 + 40 - \frac{50 \times 40}{100}) % \\ = 70 % \\ ∴ Required price of shirt \\ = (100 - 70) % of x \\ = 30 % of x \end{aligned}

78. The banker's discount on a bill due 6 months hence at 16% per annum is Rs. 216. The true discount is = ?

A. Rs. 212

B. Rs. 180

C. Rs. 210

D. Rs. 200

Discuss

Solution:

\begin{aligned} ∴ True discount is \\ = \frac{Banker's discount \times 100}{100 + rate \times time} \\ = \frac{216 \times 100}{100 + 16 \times \frac{6}{12}} \\ = \frac{21600}{108} \\ = Rs . 200 \end{aligned}

79. The cost of manufacturing of a tape recorder is Rs. 1500. The manufacturer fixes the marked price 20% above the cost of manufacture and allows a discount in such a way as to get a profit of 8%. The rate of discount is = ?

A. 12%

B. 8%

C. 20%

D. 10%

Discuss

Solution:

Cost price of tape recorder = Rs. 1500
Marked price of tape recorder

\begin{aligned} =  120 % of 1500 \\ = \frac{120}{100} \times 1500 \\ =  Rs . 1800 \end{aligned}

Selling price of tape recorder

\begin{aligned} =  108 % of 1500 \\ = \frac{108}{100} \times 1500 \\ =  Rs . 1620 \\ Rate of discount \\ = \frac{1800 - 1620}{1800} \times 100 % \\ = \frac{180}{1800} \times 100 \\ = 10 % \end{aligned}

80. For a certain article. If discount is 25% the profit is 25%. If the discount is 10%, then the profit is = ?

A. 50%

B. 40%

C. 30%

D. $33 \frac{1}{3} %$

Discuss

Solution:

\begin{aligned} For same article, \\ \frac{100 - d_{1}}{100 - d_{2}} = \frac{100 + g_{1}}{100 + g_{2}} \\ \Rightarrow \frac{100 - 25}{100 - 10} = \frac{100 + 25}{100 + g_{2}} \\ \Rightarrow \frac{75}{90} = \frac{125}{100 + g_{2}} \\ \Rightarrow 100 + g_{2} = \frac{90 \times 125}{75} \\ \Rightarrow 100 + g_{2} = 150 \\ ∴ g_{2} = 50 % \end{aligned}

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