Practice MCQ Questions and Answer on True Discount

31.

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 $$\eqalign{ & {\text{Profit }}\% = \frac{{19}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr} $$

32.

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

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

33.

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 $$\eqalign{ & \Rightarrow \frac{{80}}{{100}} \times \frac{{70}}{{100}} \times x = 2240 \cr & \Rightarrow x = {\text{Rs}}{\text{. 4000}} \cr} $$

34.

A trader wishes to gain 20% after allowing 10% discount on the marked price to his customers. At what percent higher than the cost price must he mark his goods ?

• (A) 30%
• (B) $$\text{ 33}\frac{1}{3}\mathrm{\%}$$
• (C) $$\text{34}\frac{2}{3}\mathrm{\%}$$
• (D) 35%

Show Answer

 Let the cost price of goods = Rs. 100 Selling price of goods = 120% of 100 = Rs. 120 Mark price of goods $$\eqalign{ & {\text{ = 120}} \times \frac{{100}}{{90}} \cr & = \frac{{400}}{3}{\text{ }} \cr} $$ Difference of Mark price and Cost price $$\eqalign{ & {\text{ = }}\frac{{400}}{3} - 100 \cr & {\text{Difference }}\% \cr & = \frac{{\frac{{100}}{3}}}{{100}} \times 100 \cr & = \frac{{100}}{3}\% \cr & = 33\frac{1}{3}\% \cr} $$

35.

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) $$8\frac{1}{3}\mathrm{\%}$$
• (D) 9%

Show Answer

 $$\eqalign{ & {\text{Discount }} \cr & {\text{ = 6000}} - {\text{5500 }} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Discount}}\% {\text{ }} \cr & = \frac{{500}}{{6000}} \times 100 \cr & = \frac{{50}}{6} \cr & = \frac{{25}}{3}{\text{ }} \cr & = 8\frac{1}{3}\% \cr} $$

36.

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

Show Answer

 $$\eqalign{ & {\text{Single equivalent discount}} \cr & = \left( {50 + 40 - \frac{{50 \times 40}}{{100}}} \right)\% \cr & = 70\% \cr & \therefore {\text{Required price of shirt }} \cr & {\text{ = }}\left( {100 - 70} \right)\% {\text{ of }}x \cr & = 30\% {\text{ of }}x \cr} $$

37.

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

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

38.

In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit percent of = ?

• (A) 30%
• (B) 32%
• (C) 33%
• (D) 35%

Show Answer

 CP SP MP     100×10       117×10       90×13     100×13 1000 1170 1300 $$\eqalign{ & \therefore {\text{L}}{\text{.C}}{\text{.M of 117 and 90}} \cr & {\text{Profit}} = {\text{1300}} - {\text{1000}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 300}} \cr & {\text{Profit}} = \frac{{300}}{{1000}} \times {\text{100 }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{30% }} \cr} $$

39.

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% $$\eqalign{ & = 28 + 5 - \frac{{28 \times 5}}{{100}} \cr & = 33 - 1.4 \cr & = 31.6\% \cr} $$

40.

A dealer buys an article marked at Rs. 25000 with 20% and 5% off. He spends Rs. 1000 for its repair and sells it for Rs. 25000 what is his gain or loss percent ?

• (A) Loss of 25%
• (B) Gain of 25%
• (C) Gain of 10%
• (D) Loss of 10%

Show Answer

 Marked price of an article = Rs. 25000 After discount, cost price $$ = {\text{Rs}}{\text{. 25000}} \times \frac{{80}}{{100}} \times \frac{{95}}{{100}}$$ = Rs. 19000 After repair, cost price = Rs. 19000 + 1000 = Rs. 20000 Selling price of an article = Rs. 25000 $$\eqalign{ & {\text{Gain}}\% \Rightarrow \frac{{25000 - 20000}}{{20000}} \times 100 \cr & {\text{Gain}}\% \Rightarrow \frac{1}{4} \times 100 \cr & {\text{Gain}}\% \Rightarrow 25\% \cr} $$