Practice MCQ Questions and Answer on True Discount

81.

Three successive discount of 12%, 13% and 11% are equivalent to an approximate single discount of:

• (A) 32%
• (B) 40%
• (C) 42%
• (D) 35%

Show Answer

 Equivalent discount of (12%, 13%, 11%) = ? Equivalent discount of (12% and 11%) = 12 + 11 - $$\frac{{12 \times 11}}{{100}}$$ = 23 - 1.32 = 21.68% Equivalent discount of (21.68% and 11%) = 21.68 + 11 - $$\frac{{21.68 \times 11}}{{100}}$$ = 32%

82.

The single discount equivalent to the discount series of 20%, 10% and 5% is = ?

• (A) 11.66%
• (B) 31.6%
• (C) 35.66Z%
• (D) 32%

Show Answer

 Single equivalent discount for 20% and 10% $$\eqalign{ & = 20 + 10 - \frac{{20 \times 10}}{{100}} \cr & = 30 - 2 \cr & = 28\% \cr} $$ Single equivalent discount for 28% and 5% $$\eqalign{ & = 28 + 5 - \frac{{28 \times 5}}{{100}} \cr & = 33 - 1.4 \cr & = 31.6\% \cr} $$

83.

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

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

Show Answer

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

84.

The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

• (A) Rs. 1386
• (B) Rs. 1764
• (C) Rs. 1575
• (D) Rs. 2268

Show Answer

 $$\eqalign{ & {\text{Let}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{x}}{\text{.}} \cr & {\text{Then,}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{x}}\,{\text{at}}\,{\text{16}}\% \,{\text{for}}\,{\text{9}}\,{\text{months}} \cr & = Rs.\,189 \cr & \therefore x \times 16 \times \frac{9}{{12}} \times \frac{1}{{100}} \cr & = 189\,or\,x = 1575. \cr & \therefore P.W. = Rs.\,1575. \cr & \therefore {\text{Sum}}\,{\text{due}} = P.W. + T.D. \cr & = Rs.\left( {1575 + 189} \right) \cr & = Rs.\,1764 \cr} $$

85.

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%

Show Answer

 $$\eqalign{ & {\text{Cost price for the retailer }} \cr & = 800 \times \frac{{90}}{{100}} \times \frac{{85}}{{100}} + 13 \cr & = 612 + 13 \cr & {\text{ = Rs. 625 }} \cr & {\text{Selling price = Rs}}{\text{. 875}} \cr & \therefore {\text{Profit }}\% {\text{ }} \cr & = \frac{{875 - 625}}{{625}} \times 100 \cr & = \frac{{250}}{{625}} \times 100 \cr & = 40\% \cr} $$

86.

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

Show Answer

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

87.

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

Show Answer

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

88.

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

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

89.

The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:

• (A) 6 months
• (B) 8 months
• (C) 9 months
• (D) 10 months

Show Answer

 $$\eqalign{ & P.W. = Rs.\left( {1760 - 160} \right) = Rs.\,1600 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{12}}\% \,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{160}}{\text{}} \cr & \therefore {\text{Time}} = {\frac{{100 \times 160}}{{1600 \times 12}}} \cr & = \frac{5}{6}{\text{years}} \cr & = \left( {\frac{5}{6} \times 12} \right){\text{months}} \cr & = 10\,{\text{months}}{\text{}} \cr} $$

90.

A trader marked the selling price of an article at 10% above the cost price. At the time of selling he allows certain discount and suffers a loss of 1%. He allowed the discount of ?

• (A) 11%
• (B) 10%
• (C) 9%
• (D) 10.5%

Show Answer

 Let the cost price of an article = Rs. 100 Marked price of an article = Rs. 110 (10% above) Selling price of an article = Rs. 99 (10% discount) $$\eqalign{ & {\text{Difference}} = {\text{ }}110 - 99{\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 11}} \cr & {\text{Discount}} = \frac{{11}}{{110}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$