Discount problems
- 1. A man purchased a shirt and pant with a discount of 25% on its marked price. He sold them at a price 40% more than the price at which he bought them. How much percent the new selling price to its marked price?
Options- A. 5%
- B. 7.5%
- C. 9%
- D. 12.5% Discuss
Correct Answer: 5%
Explanation:
Let the original price of pant and shirt be = ? N.
? Cost price of point and shirt = [N x (100 - 25)]/100 = ? 3N/4
And selling price of shirt and pant = (3N/4) x (100 + 40)/100 = (3N/4) x (140/100)
= ? 21N/20
Hence, required percentage
= [(21N/20 - N)/ N] x 100 % = 100 / 20 % = 5%
- 2. By selling an article at 80 % of its marked price, a trader makes a loss of 10 %, what will be a profit percentage, if he sells it at 95 % of its marked price?
Options- A. 6.9 %
- B. 5 %
- C. 5.9 %
- D. 12.5 % Discuss
Correct Answer: 6.9 %
Explanation:
Let marked price = ? 100
And selling price = ? 80
In condition of 10% loss the cost price of article = (80 x 100)/90 = ? 800/9
According to the question,
When SP = 95, then
? Required profit percentage = [{95 - (800/9)} / (800/9)] x 100 = 55/8
= 6.9% (approx)
- 3. What is the maximum percentage discount (approximately) that a merchant can offer on his marked price, so that he ends up selling at no profit or loss, if he initially marked his goods up by 40%?
Options- A. 60%
- B. 28.5%
- C. 33.5%
- D. No discount Discuss
Correct Answer: 28.5%
Explanation:
Let cost price = ? 100
And marked price = 100 + 40 = ? 140
Let required discount be R %.
According to the question,
140 x (100 - R)/100 = 100
? 100 - R = (100 x 100) / 140
? R = 100 - (100 x 100) / 140
= (40 x 100) / 140
= 28.5 % (approx)
- 4. A shopkeeper allows a discount of 10% to his customers and still gains 20%, the marked price of the article which costs ? 450, is
Options- A. ? 600
- B. ? 540
- C. ? 660
- D. ? 580 Discuss
Correct Answer: ? 600
Explanation:
Here, r = 10% and R = 20%
? Required per cent = (r + R)/(100 - r) x 100 %
= [(10 + 20)/(100 - 10)] x 100% = (30 x 100)/90 %
This shows that the marked price of the item is 100/3 % more
than its cost price.
? Marked price of the article = (450 x 400)/300
= ? 600
- 5. A dozen pair of socks quoted ? 80 are available at a discount of 10%. How many pair of socks can be bough for ? 24?
Options- A. 4
- B. 5
- C. 3
- D. 6 Discuss
Correct Answer: 4
Explanation:
? MP of one dozen of pairs of socks = ? 80
? SP of one dozen of pairs of socks
=80 x (100 - 10)/100 = 80 x 90/100= ? 72
Hence, required number of pairs of socks
purchased for ? 24 = (12 x 24)/72 = 4
- 6. A retailer offers the following discount schemes for buyers on an article .
i. Two successive discounts of 10 % .
ii. A discount of 12 % followed by a discount of 8 %.
iii. Successive discount of 15 % and 5 % .
iv. A discount of 20 % .
The selling price will be minimum under the scheme
Options- A. i
- B. ii
- C. iii
- D. iv Discuss
Correct Answer: iv
Explanation:
i. Equivalent single discount to 10 % and 10 % = 10 + 10 - (10 x 10)/100 % = 19 %
ii. Equivalent single discount to 12 % and 8 % = 12 + 8 - (12 x 8)/100 = 20 - 0.96 = 19.04 %
iii. Equivalent single discount to 15 % and 5 % = 15 + 5 - (15 x 5)/100 = 20 - 0.75 = 19.25 %
iv. Equivalent single discount to 20 % = 20 % So, the selling price will be minimum under the scheme iv as in this scheme, the discount is maximum .
- 7. The market price of a clock is ? 3200 . It is to be sold at ? 2448 at two successive discounts . If the first discount is 10 %, then the second discount is
Options- A. 5 %
- B. 10 %
- C. 15 %
- D. 20 % Discuss
Correct Answer: 15 %
Explanation:
Let rate of second discount = r %
MP = ? 3200 , SP = ? 2448 ,
r1 = 10 % and r2 = r %
? y = MP x (100 - r1/100) (100 - r2/100)
? 2448 = [3200 x (100 - 10) x (100 - r)] / (100 x 100)
? (2448 x 100 x 100) / (3200 x 90) = 100 - r
? r = 100 - 85 = 15 %
- 8. A shopkeeper sells not books at the rate of ? 457 each and earns a commission of 4% He also sells pencil boxes at the rate of ? 80 each and earns a commission of 20%. How much amount of commission will he he earn in two weeks, if he sells 10 notebooks and 6 pencil boxes a boy?
Options- A. ? 1956
- B. ? 1586
- C. ?1496
- D. ? 1596 Discuss
Correct Answer:
Explanation:
? S.P of the notebook = ?457
? Commission on one notebook = ? (4 x 457)/100
and commission on 10 notebooks = 10 x (4 x 457)/100 = ? 18280
Now,S.P of the pencil box = ? 80
? Commission on 1 pencil box = ? (80 x 20)/100
Commission on 6 pencil boxes = (80 x 20 x 6)/100 = ? 96
Hence ,total commission of 1 day = (182.80 + 96 ) = ? 278.80
Thus, total commission of 2 weeks = 278.80 x 14 = ? 3903.20
- 9. If the price of an item is increased by 30 % and then allows two successive discounts of 10 % and 10 % . In last the price of an item is?
Options- A. Increased by 10%
- B. Increased by 5.3%
- C. decreased by 3%
- D. decreased by 5.3% Discuss
Correct Answer: Increased by 5.3%
Explanation:
Let the cost price of item = ? N
? Marked price of item = N x (100 + 30)/100 = ? 13N/10
Selling price of the item after two successive discount = (13N/10) x[ (100 - 10)/100 x (100 - 10)/100]
= (13N/10) x (90/100) x (90/100) = ? 1053N/1000
Increment in the price of item = [{(1053N/1000) - N} / N] x 100 %
= 53/10 %
= 5.3 %
- 10. The difference between a discount of 30% on ? 2000 and two successive discounts of 25% and 5% on the same amount is
Options- A. ? 30
- B. ? 35
- C. ? 25
- D. ? 40 Discuss
Correct Answer: ? 25
Explanation:
Single equivalent discount per cent to 25% and 5%
= r1 + r2 - (r1 . r2)/100 %
= 25 + 5 - (25 x 5)/100
= 30 - 1.25
= 28.78 %
? Required difference = [(30 - 28.75) x 2000]/100
= 1.25 x 2000/100 = ? 25
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