Exercise : True Discount - General Questions
✔ True Discount -
General Questions
11.
A shopkeeper earns 20% profit after allowing a 10% discount. If the Cost Price (CP) is $450, find the Marked Price (MP).
View Answer
Answer: Option C
Explanation:
Explanation:
1. Calculate Selling Price (SP) using profit: \(SP = CP \times (1 + \text{Profit } \%)\).
2. \(SP = 450 \times 1.20 = 540\).
3. Relate SP to MP using discount: \(SP = MP \times (1 - \text{Discount } \%)\).
4. \(540 = MP \times 0.90\).
5. Solve for MP: \(MP = 540 / 0.90 = 600\).
6. The Marked Price is $600.
2. \(SP = 450 \times 1.20 = 540\).
3. Relate SP to MP using discount: \(SP = MP \times (1 - \text{Discount } \%)\).
4. \(540 = MP \times 0.90\).
5. Solve for MP: \(MP = 540 / 0.90 = 600\).
6. The Marked Price is $600.
12.
What percentage above the Cost Price (CP) should a man mark his goods so that after a 20% discount, he still earns 10% profit?
View Answer
Answer: Option C
Explanation:
Explanation:
1. Let CP = 100. To earn 10% profit, the Selling Price (SP) must be 110.
2. The SP is obtained after a 20% discount on the Marked Price (MP).
3. So, \(0.80 \times MP = 110\).
4. Solve for MP: \(MP = 110 / 0.80 = 137.5\).
5. The mark-up amount is \(137.5 - 100 = 37.5\).
6. Mark-up percentage = \((37.5 / 100) \times 100 = 37.5\%\).
2. The SP is obtained after a 20% discount on the Marked Price (MP).
3. So, \(0.80 \times MP = 110\).
4. Solve for MP: \(MP = 110 / 0.80 = 137.5\).
5. The mark-up amount is \(137.5 - 100 = 37.5\).
6. Mark-up percentage = \((37.5 / 100) \times 100 = 37.5\%\).
13.
A fan is listed at $1,500 and a discount of 20% is offered. What additional discount must be given to bring the net price to $1,104?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Price after the first 20% discount: \(1,500 \times 0.80 = 1,200\).
2. Target net price is $1,104.
3. Additional discount amount required: \(1,200 - 1,104 = 96\).
4. Additional discount percentage: \((96 / 1,200) \times 100 = 8\%\).
5. The additional discount needed is 8%.
2. Target net price is $1,104.
3. Additional discount amount required: \(1,200 - 1,104 = 96\).
4. Additional discount percentage: \((96 / 1,200) \times 100 = 8\%\).
5. The additional discount needed is 8%.
14.
The ratio of Cost Price (CP) to Marked Price (MP) is 2:3 and the ratio of CP to Selling Price (SP) is 4:5. Find the discount percentage.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Express both ratios with a common CP value. Given CP:MP = 2:3 and CP:SP = 4:5.
2. To make CP common, multiply the first ratio by 2: CP:MP = 4:6.
3. Now we have CP = 4, MP = 6, and SP = 5.
4. Discount amount = \(MP - SP = 6 - 5 = 1\).
5. Discount % = \((1 / 6) \times 100 = 16.67\%\).
2. To make CP common, multiply the first ratio by 2: CP:MP = 4:6.
3. Now we have CP = 4, MP = 6, and SP = 5.
4. Discount amount = \(MP - SP = 6 - 5 = 1\).
5. Discount % = \((1 / 6) \times 100 = 16.67\%\).
15.
A retailer buys an article for $1,200 after getting a 20% discount on the Marked Price (MP). He sells it for $1,600. Find his profit percentage based on the MP.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Find the MP: \(0.80 \times MP = 1,200 \implies MP = 1,200 / 0.80 = 1,500\).
2. The retailer's cost is $1,200 and he sells for $1,600.
3. Profit amount = \(1,600 - 1,200 = 400\).
4. The question asks for profit % based on the MP (not the retailer's CP).
5. Profit % (based on MP) = \((400 / 1,500) \times 100 = 26.67\%\).
2. The retailer's cost is $1,200 and he sells for $1,600.
3. Profit amount = \(1,600 - 1,200 = 400\).
4. The question asks for profit % based on the MP (not the retailer's CP).
5. Profit % (based on MP) = \((400 / 1,500) \times 100 = 26.67\%\).
16.
A merchant allows a 25% discount on Marked Price (MP) and earns 20% profit. If he gets $40 as profit, find the discount amount.
View Answer
Answer: Option C
Explanation:
Explanation:
1. Profit is 20% of CP: \(0.20 \times CP = 40 \implies CP = 40 / 0.20 = 200\).
2. Selling Price (SP) = \(CP + \text{Profit} = 200 + 40 = 240\).
3. SP is obtained after a 25% discount on MP: \(0.75 \times MP = 240\).
4. Solve for MP: \(MP = 240 / 0.75 = 320\).
5. Discount amount = \(MP - SP = 320 - 240 = 80\).
2. Selling Price (SP) = \(CP + \text{Profit} = 200 + 40 = 240\).
3. SP is obtained after a 25% discount on MP: \(0.75 \times MP = 240\).
4. Solve for MP: \(MP = 240 / 0.75 = 320\).
5. Discount amount = \(MP - SP = 320 - 240 = 80\).
17.
A trader sells at a 10% discount but uses a faulty scale that weighs 10% less. Find his overall profit percentage.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Let the original Marked Price and Cost Price for 1000g be 100.
2. He sells at a 10% discount: \(SP = 90\).
3. However, he gives 10% less weight, meaning he gives 900g instead of 1000g.
4. The Cost Price of 900g is 90 (since 1000g costs 100).
5. He sells 90 worth of goods for 90.
6. Profit = \(90 - 90 = 0\). Overall profit % is 0%.
2. He sells at a 10% discount: \(SP = 90\).
3. However, he gives 10% less weight, meaning he gives 900g instead of 1000g.
4. The Cost Price of 900g is 90 (since 1000g costs 100).
5. He sells 90 worth of goods for 90.
6. Profit = \(90 - 90 = 0\). Overall profit % is 0%.
18.
A shopkeeper gives 3 consecutive discounts of x%, 20%, and 10%. If the total discount is 46%, find x.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Total discount is 46%, so the remaining price factor is \(1 - 0.46 = 0.54\).
2. The product of the remaining factors for each discount must equal 0.54.
3. \((1 - x/100) \times (1 - 0.20) \times (1 - 0.10) = 0.54\).
4. \((1 - x/100) \times 0.80 \times 0.90 = 0.54\).
5. \((1 - x/100) \times 0.72 = 0.54\).
6. \(1 - x/100 = 0.54 / 0.72 = 0.75\).
7. \(x/100 = 0.25 \implies x = 25\).
2. The product of the remaining factors for each discount must equal 0.54.
3. \((1 - x/100) \times (1 - 0.20) \times (1 - 0.10) = 0.54\).
4. \((1 - x/100) \times 0.80 \times 0.90 = 0.54\).
5. \((1 - x/100) \times 0.72 = 0.54\).
6. \(1 - x/100 = 0.54 / 0.72 = 0.75\).
7. \(x/100 = 0.25 \implies x = 25\).
19.
The difference between a single discount of 35% and two successive discounts of 20% and 15% on a certain amount is $24. Find the amount.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Single discount = 35%.
2. Successive discounts of 20% and 15%: \(20 + 15 - (20 \times 15)/100 = 35 - 3 = 32\%\).
3. Difference in percentage: \(35\% - 32\% = 3\%\).
4. We are given \(3\% \text{ of } MP = 24\).
5. \(0.03 \times MP = 24 \implies MP = 24 / 0.03 = 800\).
6. The amount is $800.
2. Successive discounts of 20% and 15%: \(20 + 15 - (20 \times 15)/100 = 35 - 3 = 32\%\).
3. Difference in percentage: \(35\% - 32\% = 3\%\).
4. We are given \(3\% \text{ of } MP = 24\).
5. \(0.03 \times MP = 24 \implies MP = 24 / 0.03 = 800\).
6. The amount is $800.
20.
A company offers three schemes: (i) 25% and 15%, (ii) 30% and 10%, (iii) 35% and 5%. Which is best for the customer?
View Answer
Answer: Option C
Explanation:
Explanation:
1. Calculate single equivalent discount for each.
2. Scheme 1: \(25 + 15 - (25 \times 15)/100 = 40 - 3.75 = 36.25\%\).
3. Scheme 2: \(30 + 10 - (30 \times 10)/100 = 40 - 3 = 37\%\).
4. Scheme 3: \(35 + 5 - (35 \times 5)/100 = 40 - 1.75 = 38.25\%\).
5. Higher discount is better for the customer. Scheme (iii) offers 38.25%.
2. Scheme 1: \(25 + 15 - (25 \times 15)/100 = 40 - 3.75 = 36.25\%\).
3. Scheme 2: \(30 + 10 - (30 \times 10)/100 = 40 - 3 = 37\%\).
4. Scheme 3: \(35 + 5 - (35 \times 5)/100 = 40 - 1.75 = 38.25\%\).
5. Higher discount is better for the customer. Scheme (iii) offers 38.25%.