Practice MCQ Questions and Answer on True Discount

41.

An article is sold at a discount of 20% and an additional discount 30% is allowed on cash payment. If Vidya purchased the article by paying Rs. 2240 in cash, the marked price of the article was = ?

• (A) Rs. 4000
• (B) Rs. 4368
• (C) Rs. 4400
• (D) Rs. 4480

Show Answer

 Marked price of the article = Rs. x According to the question,   $$⇒$$ 80% of 70% of x = 2240 $$\eqalign{ & \Rightarrow \frac{{80}}{{100}} \times \frac{{70}}{{100}} \times x = 2240 \cr & \Rightarrow x = {\text{Rs}}{\text{. 4000}} \cr} $$

42.

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% $$\eqalign{ & = 36 + 10 - \frac{{36 \times 10}}{{100}} \cr & = 46 - 3.6 \cr & = 42.4\% \cr} $$

43.

A owes B, Rs. 1573 payable $$\text{1}\frac{\text{1}}{\text{2}}$$ years hence. Also B owes A, Rs. 1444.50 payable 6 months hence. If they want to settle the account forthwith, keeping 14% as the rate of interest, then who should pay and how much ?

• (A) A Rs. 28.50
• (B) B Rs. 37.50
• (C) A Rs. 50
• (D) B Rs. 50

Show Answer

 A owes = P.W. of Rs. 1573 due $$\frac{3}{2}$$ years hence $$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left[ {\frac{{1573 \times 100}}{{100 + \left( {14 \times \frac{3}{2}} \right)}}} \right]\, \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{1573 \times 100}}{{121}}} \right) \cr & = {\text{Rs}}{\text{.}}\,1300. \cr} $$ B owes = P.W. of Rs. 1444.50 due 6 months hence $$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left[ {\frac{{1444.50 \times 100}}{{100 + \left( {14 \times \frac{1}{2}} \right)}}} \right]\, \cr & = \,{\text{Rs}}{\text{.}}\,\left( {\frac{{1444.50 \times 100}}{{107}}} \right) \cr & = {\text{Rs}}{\text{.}}\,1350. \cr & \therefore \,{\text{B}}\,{\text{must}}\,{\text{pay}}\,{\text{Rs}}{\text{.}}\,\,{\text{50}}\,{\text{to}}\,{\text{A}} \cr} $$

44.

Anand marks up the price of an article by 50% and then allows a discount of 20% and sells it to Balaji who sells it for Rs. 20, more than what he purchased for, this selling price is 30% more then the original cost price of the article. Then Balaji's profit % is = ?

• (A) 7.5%
• (B) 6.66%
• (C) 8.33%
• (D) 9%

Show Answer

 Let original cost price = 100 units $$\eqalign{ & {\text{Cost price of Balaji }} \cr & {\text{ = 100}} \times \frac{{150}}{{100}} \times \frac{{80}}{{100}} \cr & {\text{ = 120 units}} \cr & {\text{Selling price of Balaji }} \cr & {\text{ = }}\frac{{130}}{{100}} \times 100\, \cr & {\text{ = 130 units}} \cr & {\text{Profit of Balaji }} \cr & {\text{ = 130}} - 120 \cr & = {\text{10 units}} \cr & {\text{Profit percent }} \cr & {\text{ = }}\frac{{10}}{{120}} \times 100 \cr & {\text{ = 8}}{\text{.33}}\% \cr} $$ Note: There is no use of Rs. 20 given in the question

45.

If the selling price of an article is 32% more than its cost price and the discount offered on its marked price is 12%, then what is the ratio of its cost price to the marked price?

• (A) 2 : 3
• (B) 4 : 5
• (C) 3 : 8
• (D) 1 : 2

Show Answer

 $$32\% \to \frac{{ + 8}}{{25}},\,\,12\% \to \frac{{ - 3}}{{25}}$$ \[\begin{array}{*{20}{c}} {{\text{Cost price }}\,\,\,{\text{ Selling price }}\,\,\,{\text{ Marked price}}} \\ {{{25}_{ \times 2}}\,\,\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,\,{{33}_{ \times 2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{22}_{ \times 3}}\,\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,{{25}_{ \times 3}}} \\ {\overline {\,\,50\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,66\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,\,\,75\,\,\,\,\,\,\,\,} } \end{array}\] $${\text{Cost price}}:{\text{Marked price}} = 2:3$$

46.

A discount of 14% on the marked price of an article is allowed and then the article is sold for Rs. 387. The marked price of the article is = ?

• (A) Rs. 450
• (B) Rs. 427
• (C) Rs. 500
• (D) Rs. 440

Show Answer

 Selling price of article = Rs. 387 Mark price of article $$\eqalign{ & {\text{ = }}\frac{{387 \times 100}}{{86}} \cr & = {\text{Rs}}{\text{. 450}} \cr} $$

47.

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

48.

A purchased a dining table marked at Rs. 3000 at a successive discounts of 10% and 15% respectively. He gave Rs. 105 as trans-portion charge and sold it at Rs. 3200. What is his gain percentage ?

• (A) $$22\frac{1}{3}\mathrm{\%}$$
• (B) 25%
• (C) $$33\frac{1}{3}\mathrm{\%}$$
• (D) $$37\frac{17}{24}\mathrm{\%}$$

Show Answer

 Market price of dining table = Rs. 3000 After discount, cost price $$\eqalign{ & {\text{ = 3000}} \times \frac{{90}}{{100}} \times \frac{{85}}{{100}} \cr & {\text{ = Rs}}{\text{. 2295}} \cr} $$ After transport charges = 2295 + 105 $$\eqalign{ & {\text{Cost price = Rs}}{\text{. 2400}} \cr & {\text{Selling price = Rs}}{\text{. 3200}} \cr & {\text{Profit }}\% {\text{ }} \cr & = \frac{{3200 - 2400}}{{2400}} \times 100 \cr & = \frac{{800 \times 100}}{{2400}} \cr & = 33\frac{1}{3}\% \cr} $$

49.

The single discount equal to three consecutive discounts of 10%, 12% and 5% ?

• (A) 35%
• (B) 32%
• (C) 24.76%
• (D) 30%

Show Answer

 Let the marked price Rs. 100 $$\eqalign{ & {\text{Final selling price}} \cr & {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{88}}{{100}} \times \frac{{95}}{{100}} \cr & {\text{ = Rs}}{\text{. 75}}{\text{.24 }} \cr & {\text{Net discount }} \cr & {\text{ = }}\left( {100 - 75.24} \right) \cr & {\text{ = 24}}{\text{.76}}\% \cr} $$ Alternate : Single equivalent discount for 10% and 12% $$\eqalign{ & = \left( {10 + 12 - \frac{{10 \times 12}}{{100}}} \right)\% \cr & = 20.8\% \cr} $$ Single equivalent discount for 20.8% and 5% $$\eqalign{ & = \left( {20.8 + 5 - \frac{{20.8 \times 5}}{{100}}} \right)\% \cr & = 24.76\% \cr} $$

50.

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

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