Practice MCQ Questions and Answer on True Discount

11.

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

• (A) 10%
• (B) $$10\frac{1}{2}\mathrm{\%}$$
• (C) 20%
• (D) 12%

Show Answer

 $$\eqalign{ & {\text{Discount }}\% \cr & = \frac{{440 - 396}}{{440}} \times 100 \cr & = 10\% \cr} $$

12.

Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:

• (A) $$16\frac{2}{3}$$%
• (B) $$14\frac{1}{2}$$%
• (C) $$13\frac{1}{3}$$%
• (D) 15%

Show Answer

 $$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = 102\% \,of\,Rs.\,600 \cr & = {\frac{{102}}{{100}} \times 600} \cr & = Rs.\,612 \cr & {\text{Now,}}\,\cr & {\text{P}}{\text{.W}}{\text{. = Rs}}{\text{. 612}}\,{\text{and}}\,{\text{sum}} = Rs.\,688.50 \cr & \therefore {\text{T}}{\text{.D}}{\text{.}} = Rs.\,\left( {688.50 - 612} \right) \cr & = Rs.\,76.50. \cr & {\text{Thus,}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{612}}\,{\text{for}}\,{\text{9}}\,{\text{months}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{76}}{\text{.50}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 76.50}}{{612 \times \frac{3}{4}}}} \right)\% \cr & = 16\frac{2}{3}\% \, \cr} $$

13.

A person sells an article at 16% below its cost price. Had he sold it for Rs. 33 more, he would have gained 14%. To gain 25% he should sell the article for:

• (A) Rs. 128
• (B) Rs. 137.50
• (C) Rs. 135
• (D) Rs. 130.50

Show Answer

 $$\eqalign{ & {\text{Let cost price}} = x \cr & x \times \frac{{114}}{{100}} - \frac{{x \times 84}}{{100}} = 33 \cr & x \times 30 = 33 \times 100 \cr & x = 110 \cr & {\text{To gain }}25\% , \cr & {\text{Selling price}} = \frac{{110 \times 125}}{{100}} = 137.50 \cr} $$

14.

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 $$\eqalign{ & {\text{ So, the 2nd discount be}}\% \cr & = \frac{{15200 - 11400}}{{15200}} \times 100 \cr & = \frac{{3800}}{{15200}} \times 100 \cr & = 25\% \cr} $$

15.

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%

Show Answer

 Let the cost price = 100 units Marked price = 140 units Selling price = 140 × $$\frac{{85}}{{100}}$$   = 119 $$\eqalign{ & {\text{Profit }}\% = \frac{{19}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr} $$

16.

A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash is = ?

• (A) 10.5%
• (B) 15%
• (C) 9%
• (D) 8.5%

Show Answer

 Let cost price of item = Rs. 100 Marked price of item = 130% of 100 $$\eqalign{ & {\text{ = 130}}\% {\text{ of 100}} \cr & {\text{ = }}\frac{{130}}{{100}} \times {\text{100 }} \cr & {\text{ = Rs}}{\text{. 130 }} \cr} $$ After discount, selling price $$\eqalign{ & {\text{= 85}}\% {\text{ of 130 }} \cr & = \frac{{85}}{{100}} \times {\text{130 }} \cr & {\text{= Rs}}{\text{. 110}}{\text{.5}} \cr & {\text{Profit}}\% {\text{ }} \cr & = \frac{{110.50 - 100}}{{100}} \times 100{\text{ }} \cr & = 10.5{\text{ }}\% {\text{ }} \cr} $$

17.

A shopkeeper marks the price of an article at Rs. 80. What will be the selling price, if he allows two successive discounts at 5% each = ?

• (A) Rs. 72.20
• (B) Rs. 72
• (C) Rs. 85
• (D) Rs. 7.20

Show Answer

 Marked price of article = Rs. 80 $$\eqalign{ & {\text{Two successive discount }} \cr & {\text{ = 5}} + 5 - \frac{{5 \times 5}}{{100}} \cr & = 10 - 0.25 \cr & = 9.75\% \cr & {\text{Discount of article }} \cr & {\text{ = 9}}{\text{.75% of 80}} \cr & {\text{ = }}\frac{{9.75}}{{100}} \times 80 \cr & = {\text{Rs}}{\text{. 7}}{\text{.80}} \cr & {\text{Selling price of article }} \cr & {\text{ = }}80 - 7.80 \cr & {\text{ = Rs}}{\text{. 72}}{\text{.20}} \cr} $$

18.

The present worth of Rs. 2310 due $$2\frac{1}{2}$$ years hence, the rate of interest being 15% per annum, is:

• (A) Rs. 1750
• (B) Rs. 1680
• (C) Rs. 1840
• (D) Rs. 1443.75

Show Answer

 $$\eqalign{ & P.W. = Rs.\,\left[ {\frac{{100 \times 2310}}{{100 + \left( {15 \times \frac{5}{2}} \right)}}} \right] \cr & = Rs.\,1680 \cr} $$

19.

A single discount equivalent to discount series 20% , 20% and 10% is = ?

• (A) 50%
• (B) 48.4%
• (C) 42.4%
• (D) 40.4%

Show Answer

 Single equivalent discount for 20% and 20% $$\eqalign{ & = 20 + 20 - \frac{{20 \times 20}}{{100}} \cr & = 40 - 4 \cr & = 36\% \cr} $$ Single equivalent discount for 36% and 10% $$\eqalign{ & = 36 + 10 - \frac{{36 \times 10}}{{100}} \cr & = 46 - 3.6 \cr & = 42.4\% \cr} $$

20.

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

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