# Mathematics Questions and Answers – Finding Discounts

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Finding Discounts”.

1. A bag marked at a price of Rs. 1600 is available at a discount of 45%. What is the discount given?
a) Rs 740
b) Rs 720
c) Rs 800
d) Rs 760

Explanation: Discount offered = 45%
Marked price of bag = Rs. 1600
Discount = 45%
= 45% of 1600
= $$\frac{45}{100}$$ × 1600 = 720
The discount given is Rs. 720

2. At a clothing store, Ameena buys a pair of jeans and some t-shirts marked at a price of Rs. 2500 at 50% discount. How much does she need to pay to the shopkeeper?
a) Rs 1600
b) Rs 1250
c) Rs 1750
d) Rs 1800

Explanation: Discount offered = 50%
Marked price of all the items = Rs. 2500
Discount = 50%
= 50% of 2500
= $$\frac{50}{100}$$ × 2500 = 1250
The discount given is Rs. 1250
Sale Price = Marked Price – Discount
= 2500 – 1250 = 1250
Ameena has to pay Rs. 1250 to the shopkeeper.

3. At a shopping bonanza a 55% discount is offered on all its items. What would be the sale price of a shoe marked at Rs. 5000?
a) Rs 2250
b) Rs 2500
c) Rs 5000
d) Rs 2750

Explanation: Discount offered = 55 %
Marked price of shoe = Rs. 5000
Discount = 55%
= 55% of 5000
= $$\frac{55}{100}$$ × 5000 = 2750
The discount given is Rs. 2750.
Sales price = Marked Price – discount
= 5000 – 2750
= 2250
The sale price of the shoe will be Rs. 2250

4. An almirah is marked is marked at Rs. 17,000 is sold at Rs. 10,000. What is the discount given?
a) 48.9%
b) 45.7%
c) 42.6%
d) 41.17 %

Explanation: Marked price of almirah = Rs. 17000
Sale price of the almirah = Rs. 10000
Discount = Marked price – Sale price
= 17000 – 10000
= 7000
Discount % = $$\frac{7000}{17000}$$ × 100 = 41.17%

5. 10 books each of Rs. 300 are sold at Rs. 2500. What is the percentage of the discount given?
a) 11.2 %
b) 17.9 %
c) 16.67%
d) 16.85%

Explanation: Marked price of 1 book = Rs. 300
Marked price of 10 books = Rs. 3000
Sale price of the almirah = Rs. 2500
Discount = Marked price – Sale price
= 3000 – 2500
= 500
Discount % = $$\frac{500}{3000}$$ × 100 = 16.67 %

6. A dinner set is sold at Rs. 4500 after giving a discount of 15%. What is the marked price of the dinner set?
a) Rs 4600
b) Rs 4700
c) Rs 4000
d) Rs 4800

Explanation: Sale price of the dinner set = Rs. 4500
Discount given = 15%
Let the marked price be Rs. x
Discount = 15% of x
= $$\frac{15}{100}$$ × x = $$\frac{5x}{100}$$
Sale price = Marked price – discount
4500 = x – $$\frac{5x}{100}$$
4500 = $$\frac{95x}{100}$$
x = $$\frac{4500 × 100}{95}$$ = 4736.84 ∼ Rs. 4700
The marked price of the dinner set is Rs. 4700

7. An article was sold after offering two successive discounts of 250 and 340. If the mark price of is 1000 then what is the selling price of the article?
a) Rs 495
b) Rs 500
c) Rs 300
d) Rs 465

Explanation: Discount given = 250 and 340.
Marked price = Rs.1000
First discount % = $$\frac{250}{1000}$$ × 100 = 25%
Second discount % = $$\frac{340}{1000}$$ × 100 = 34%
We know that, if when an article is sold after two successive discounts of x% and y%, then the final selling price = $$\frac{Marked \, Price × (100-x) × (100-y)}{100 × 100}$$
Here two successive discounts of 25% and 34% are given,
Therefore the sales price = $$\frac{1000×(100-25)×(100-34)}{100×100}$$ = 495
The selling price of the article is Rs. 495

8. A pen is sold for Rs. 1500 after offering two successive discounts of 5% and 7%. What is the marked price of the shirt?
a) Rs 1500
b) Rs 1600
c) Rs 1700
d) Rs 1200

Explanation: We know that, if when an article is sold after two successive discounts of x% and y%, then the final selling price = $$\frac{Marked \, Price × (100-x) × (100-y)}{100 × 100}$$
Here two successive discounts of 5% and 7% are given,
Let the marked price be a
Therefore, the sales price = $$\frac{a×(100-5)×(100-7)}{100×100} = \frac{1767a}{2000}$$
Selling price = 1500
1500 = $$\frac{1767a}{2000}$$
a = 1697.79 ∼ 1700
The marked price of the article is Rs. 1700

9. The marked price of a mobile is Rs 40000. The shopkeeper allowed a discount of 30% but the customer bargained for 45%. So the shopkeeper allowed 30% and 15% successive discounts. Which of the following statements is true?
a) The shopkeeper benefitted the deal by 1200
b) The customer gained by 1800
c) The shopkeeper had a loss of 1000
d) Both parties benefitted equally

Explanation: Case I: The shopkeeper offers a 45% discount
Marked price = Rs 40000
Discount = 45%
= 45% of 40000
= $$\frac{45}{100}$$ × 40000 = 18000
Sale price = Marked price – discount = 40000 – 18000 = 22000
Case II: The shopkeeper offers two successive discounts of 30% and 15%
Here two successive discounts of 30% and 15% are given,
The marked price is 40000
Therefore, the sales price = $$\frac{40000×(100-30)×(100-15)}{100×100}$$ = 23800
Clearly, the customer benefitted from the second deal by 1800 rupees.

10. The cost price of a vintage clock is Rs 12000 and its marked price is Rs 15000. If the shopkeeper sells it at a gain of 9%, then hat is the rate of discount offered by him?
a) 9.8%
b) 11.3%
c) 10%
d) 12.8 %

Explanation: Let the discount given by him be x %.
To find out the discount given we first have to calculate the selling price of the clock.
Selling price when cost price and profit % are given (SP) = cost price ($$\frac{100+profit \, percentage}{100}$$)
Selling price = 12000($$\frac{100+9}{100}$$) = 12000(1.09) = 13080
Now, discount = Marked price – selling price = 15000 – 13080 = 1920
Discount % = $$\frac{discount}{marked \,price}$$ × 100 = $$\frac{1920}{15000}$$ × 100 = 12.8% 