Discount problems
- 1. If $ 10 be allowed as true discount on a bill of $ 110 due at the end of certain time, then the discount allowed on the same amount due at the end of double the time is :
Options- A. $ 20
- B. $ 21.81
- C. $ 22
- D. $ 18.33 Discuss
Correct Answer: $ 18.33
Explanation:
- 2. If on a marked price, the difference of selling prices with a discount of 30 % and two successive discounts of 20 % and 10 % is ? 72, then the marked price (in ?) is
Options- A. ? 3600
- B. ? 3000
- C. ? 2500
- D. ? 2400 Discuss
Correct Answer: ? 3600
Explanation:
Let the marked price = ? N
The discount equivalent to successive discounts 20 % and 10 % = { r1 + r2 - (r1 r2)/100 } %
Where, r1 = 20 and r2 = 10
Then, 30 - 2 = 28 %
According to the question,
{(100 - 28)N}/100 - {(100 - 30)N}/100 = 72
? (72N - 70N)/100 = 72
? N = (72 x 100)/2 = ? 3600
- 3. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
Options- A. 45 : 56
- B. 8 : 11
- C. 47 : 56
- D. 3 : 4 Discuss
Correct Answer: 45 : 56
Explanation:
Let the CP of book = ? P
Then, SP of book = {(100 + 12) x P}/100 = 112P/100
Now, the printed price = ? Q
Then, after discount,
the SP = (100 - 10)Q/100 = 90Q/100
Since, both SP are same.
Then, 112P/100 = 90Q/100
? P/Q = 45/56
? 45 : 56
- 4. A manufacturer marked an article at ? 50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was
Options- A. ? 40
- B. ? 35
- C. ? 32
- D. ? 30 Discuss
Correct Answer: ? 32
Explanation:
? Marked price of an article = ? 50
? SP of an article = 50 x (100 - 20)/100
= (50 x 80)/100
= ? 40
Hence, cost price of an article = (40 x 100)/(100 + 25)
= (40 x 100)/125
= ? 32
- 5. 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?
Options- A. 10.5%
- B. 15%
- C. 9%
- D. 8.5% Discuss
Correct Answer: 10.5%
Explanation:
Let CP of the goods = ? N
? Marked price of the goods = N x {(100 + 30)/100} = ? 13N/10
Now, SP of the goods = (13N/10) x (100 - 15/100)
= (13N/10) x (85/100) = ? 221N/200
? Profit = {(221 x N)/200} - N = ? 21N/200
Hence, profit per cent = [{21N/200} /N] x 100 % = 2100/200 = 10.5 %
- 6. By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is
Options- A. 5 : 3
- B. 3 : 5
- C. 3 : 4
- D. 4 : 3 Discuss
Correct Answer: 5 : 3
Explanation:
Let MP of an article = ? R
? SP of an article = ? 3R/4
and CP of an article
= (3R/4) x {100/(100 + 25)}
= 3R/4 x (100/125)
= ? 3R/5
Required ratio = R : 3R/5 = 5 : 3
- 7. While selling, businessman allows 40% discount on thee marked price and there is a loss of 30%. If it is sold at the marked price, profit per cent will be
Options- A. 10%
- B. 20%
- C. 162/3%
- D. 161/3% Discuss
Correct Answer: 162/3%
Explanation:
Let MP of an article = ? N
? SP of an article = N x (100 - 40)/100 = ? 3N / 5
CP of an article = {(3N/5) x 100}/{100 - 30}
= (3N/5) x (100/70) = ? 6N/7.
? Profit when sold at MP = N - (6N/7) = ? N/7
Hence, profit per cent = [(N/7) / (6N/7)] x 100% = 50/3%
= 162/3%
- 8. A man bought an article listed at ? 1500 with a discount of 20 % offered on the list price . What additional discount must be offered to the man to bring the net price to ? 1104?
Options- A. 8 %
- B. 10 %
- C. 12 %
- D. 15 % Discuss
Correct Answer: 8 %
Explanation:
? Listed price of an article = ? 1500
? Price after first discount
= 1500 x (1 -20/100) = 1500 x 4/5 = ? 1200
Now, second discount = 1200 - 1104 = ? 96
Hence, required percentage = (96/1200) x 100 % = 8 %
- 9. The cost price of an article is ? 800 . After allowing a discount of 10 %, a gain of 12.5 % was made . Then, the marked price of the article is
Options- A. ? 1000
- B. ? 1100
- C. ? 1200
- D. ? 1300 Discuss
Correct Answer: ? 1000
Explanation:
Here, CP = ? 800 , r = 10 % and R = 12.5 %
? Marked price (MP) = CP x (100 + R)/(100 - r)
= 800 x (100 + 12.5)/(100 - 10)
= (800 x 112.5)/90 = ? 1000
- 10. The marked price of a radio is ? 480 . The shopkeeper allows a discount of 10 % and gains 8 % . If no discount is allowed, his gain percent would be
Options- A. 18 %
- B. 18.5 %
- C. 20.5 %
- D. 20 % Discuss
Correct Answer: 20 %
Explanation:
Here, MP = ? 480 , r = 10 % and R = 8 %
? CP = MP x (100 - r)/(100 + R)
= 480 x (100 - 10)/(100 + 8) = (480 x 90)/108 = ? 400
? Profit = 480 - 400 = ? 80
Hence, profit percent = (80/400) x 100 % = 20 %
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