Exercise : True Discount - General Questions
✔ True Discount -
General Questions
21.
A dealer marks up his goods by 80% and gives a discount of 25%. Besides this, he cheats his supplier by 20% and his customer by 10%. Find his overall profit percentage.
View Answer
Answer: Option C
Explanation:
Explanation:
1. Markup and Discount effect: \(1.80 \times 0.75 = 1.35\).
2. Cheating supplier: He gets 120 units but pays for 100. Multiplier = \(120/100 = 1.2\).
3. Cheating customer: He gives 90 units but charges for 100. Multiplier = \(100/90 = 1.11...\).
4. Overall multiplier: \(1.35 \times 1.2 \times (100 / 90) = 1.62 \times (10 / 9) = 1.8\).
5. A multiplier of 1.8 corresponds to an 80% profit.
2. Cheating supplier: He gets 120 units but pays for 100. Multiplier = \(120/100 = 1.2\).
3. Cheating customer: He gives 90 units but charges for 100. Multiplier = \(100/90 = 1.11...\).
4. Overall multiplier: \(1.35 \times 1.2 \times (100 / 90) = 1.62 \times (10 / 9) = 1.8\).
5. A multiplier of 1.8 corresponds to an 80% profit.
22.
The Marked Price (MP) of an article is 50% above Cost Price (CP). When the discount is doubled, the profit reduces from $150 to $50. Find the CP.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let \(CP = 100x\), then \(MP = 150x\).
2. Case 1: \(SP_1 = MP - D = CP + 150 \implies 150x - D = 100x + 150 \implies 50x - D = 150\).
3. Case 2: \(SP_2 = MP - 2D = CP + 50 \implies 150x - 2D = 100x + 50 \implies 50x - 2D = 50\).
4. Subtract Case 2 from Case 1: \((50x - D) - (50x - 2D) = 150 - 50 \implies D = 100\).
5. Substitute D in Case 1: \(50x - 100 = 150 \implies 50x = 250 \implies x = 5\).
6. \(CP = 100x = 100 \times 5 = 500\).
2. Case 1: \(SP_1 = MP - D = CP + 150 \implies 150x - D = 100x + 150 \implies 50x - D = 150\).
3. Case 2: \(SP_2 = MP - 2D = CP + 50 \implies 150x - 2D = 100x + 50 \implies 50x - 2D = 50\).
4. Subtract Case 2 from Case 1: \((50x - D) - (50x - 2D) = 150 - 50 \implies D = 100\).
5. Substitute D in Case 1: \(50x - 100 = 150 \implies 50x = 250 \implies x = 5\).
6. \(CP = 100x = 100 \times 5 = 500\).
23.
A shopkeeper allows a discount of 10% on the Marked Price (MP) and still makes a profit of 17%. If he had allowed no discount, what would his profit percentage be?
View Answer
Answer: Option C
Explanation:
Explanation:
1. Let CP be 100. Profit is 17%, so SP = 117.
2. SP is 90% of MP: \(0.90 \times MP = 117\).
3. \(MP = 117 / 0.90 = 130\).
4. If no discount is allowed, \(SP = MP = 130\).
5. Profit = \(130 - 100 = 30\).
6. Profit % = 30%.
2. SP is 90% of MP: \(0.90 \times MP = 117\).
3. \(MP = 117 / 0.90 = 130\).
4. If no discount is allowed, \(SP = MP = 130\).
5. Profit = \(130 - 100 = 30\).
6. Profit % = 30%.
24.
After allowing a discount of 11.11%, a trader makes a profit of 14.28%. By how much percent is the Marked Price (MP) above the Cost Price (CP)?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Discount 11.11% = 1/9. Remaining factor = 8/9. So, \(SP = (8/9)MP\).
2. Profit 14.28% = 1/7. Profit factor = 1 + 1/7 = 8/7. So, \(SP = (8/7)CP\).
3. Equate SP: \((8/9)MP = (8/7)CP\).
4. \(MP/CP = (8/7) \times (9/8) = 9/7\).
5. Mark-up = \(9/7 - 1 = 2/7\).
6. \(2/7 \times 100 \approx 28.57\%\).
2. Profit 14.28% = 1/7. Profit factor = 1 + 1/7 = 8/7. So, \(SP = (8/7)CP\).
3. Equate SP: \((8/9)MP = (8/7)CP\).
4. \(MP/CP = (8/7) \times (9/8) = 9/7\).
5. Mark-up = \(9/7 - 1 = 2/7\).
6. \(2/7 \times 100 \approx 28.57\%\).
25.
A man bought an article with a 20% discount on the Marked Price (MP). He sold it with a 20% profit on the price he bought it. What is the result with respect to the original MP?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let the original MP = 100.
2. He buys it for 20% less: \(CP = 80\).
3. He sells it for 20% profit on his purchase price: \(SP = 80 \times 1.20 = 96\).
4. Compare SP to original MP: \(SP = 96\), \(MP = 100\).
5. \(100 - 96 = 4\). This is a 4% loss relative to the original Marked Price.
2. He buys it for 20% less: \(CP = 80\).
3. He sells it for 20% profit on his purchase price: \(SP = 80 \times 1.20 = 96\).
4. Compare SP to original MP: \(SP = 96\), \(MP = 100\).
5. \(100 - 96 = 4\). This is a 4% loss relative to the original Marked Price.
26.
A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
View Answer
Answer: Option A
Explanation:
Explanation:
Selling price = Rs. 3600.<br>
Present Worth (P.W.) of Rs. 3600 due 2 years hence =
\($\frac{100 \times 3600}{100 + (10 \times 2)}\)$ = Rs. 3000.<br>
Since P.W. of S.P. = C.P. there is no gain or loss.<br>
Gain = 0%.
Present Worth (P.W.) of Rs. 3600 due 2 years hence =
\($\frac{100 \times 3600}{100 + (10 \times 2)}\)$ = Rs. 3000.<br>
Since P.W. of S.P. = C.P. there is no gain or loss.<br>
Gain = 0%.