Exercise : True Discount - General Questions
✔ True Discount -
General Questions
1.
Find the Selling Price (SP) of an item if the Marked Price (MP) is $1,000 and a discount of 10% is allowed.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Calculate the discount amount: \(10\% \text{ of } 1,000 = 0.10 \times 1,000 = 100\).
2. Subtract the discount from the Marked Price to find the Selling Price: \(SP = MP - \text{Discount}\).
3. \(SP = 1,000 - 100 = 900\).
4. Therefore, the Selling Price is $900.
2. Subtract the discount from the Marked Price to find the Selling Price: \(SP = MP - \text{Discount}\).
3. \(SP = 1,000 - 100 = 900\).
4. Therefore, the Selling Price is $900.
2.
A shirt marked at $500 is sold for $425. Find the discount percentage.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Determine the discount amount: \(\text{Discount} = MP - SP = 500 - 425 = 75\).
2. Use the discount percentage formula: \(\text{Discount } \% = (\text{Discount Amount} / MP) \times 100\).
3. Substitute the values: \((75 / 500) \times 100 = 0.15 \times 100 = 15\%\).
4. The discount percentage is 15%.
2. Use the discount percentage formula: \(\text{Discount } \% = (\text{Discount Amount} / MP) \times 100\).
3. Substitute the values: \((75 / 500) \times 100 = 0.15 \times 100 = 15\%\).
4. The discount percentage is 15%.
3.
If a 20% discount on a book reduces the price by $40, find the Marked Price (MP).
View Answer
Answer: Option B
Explanation:
Explanation:
1. We are given that 20% of the MP is equal to $40.
2. Express this as an equation: \(0.20 \times MP = 40\).
3. Solve for MP: \(MP = 40 / 0.20\).
4. \(MP = 200\).
5. The Marked Price of the book is $200.
2. Express this as an equation: \(0.20 \times MP = 40\).
3. Solve for MP: \(MP = 40 / 0.20\).
4. \(MP = 200\).
5. The Marked Price of the book is $200.
4.
Find the Selling Price (SP) if the Marked Price (MP) is $1,200 and a discount of 12.5% is allowed.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Convert the discount percentage to a fraction: \(12.5\% = 1/8\).
2. Calculate the discount amount: \(1/8 \text{ of } 1,200 = 150\).
3. Subtract the discount from the MP: \(SP = 1,200 - 150\).
4. \(SP = 1,050\).
5. The Selling Price is $1,050.
2. Calculate the discount amount: \(1/8 \text{ of } 1,200 = 150\).
3. Subtract the discount from the MP: \(SP = 1,200 - 150\).
4. \(SP = 1,050\).
5. The Selling Price is $1,050.
5.
A shopkeeper offers a 'Buy 4, Get 1 Free' scheme. What is the effective discount percentage?
View Answer
Answer: Option A
Explanation:
Explanation:
1. Identify the total number of items received by the customer: \(4 + 1 = 5\).
2. Identify the number of free items: \(1\).
3. The discount is essentially the ratio of free items to the total items received.
4. \(\text{Discount } \% = (1 / 5) \times 100 = 20\%\).
5. The effective discount is 20%.
2. Identify the number of free items: \(1\).
3. The discount is essentially the ratio of free items to the total items received.
4. \(\text{Discount } \% = (1 / 5) \times 100 = 20\%\).
5. The effective discount is 20%.
6.
Find a single discount equivalent to two successive discounts of 20% and 10%.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Assume the Marked Price (MP) is 100.
2. Apply the first discount of 20%: \(100 - (0.20 \times 100) = 80\).
3. Apply the second discount of 10% on the reduced price: \(80 - (0.10 \times 80) = 80 - 8 = 72\).
4. Calculate the total discount: \(100 - 72 = 28\).
5. The single equivalent discount is 28%.
2. Apply the first discount of 20%: \(100 - (0.20 \times 100) = 80\).
3. Apply the second discount of 10% on the reduced price: \(80 - (0.10 \times 80) = 80 - 8 = 72\).
4. Calculate the total discount: \(100 - 72 = 28\).
5. The single equivalent discount is 28%.
7.
An item is sold for $576 after a 20% discount. What was the original Marked Price?
View Answer
Answer: Option C
Explanation:
Explanation:
1. Let the Marked Price be \(MP\).
2. A 20% discount means the Selling Price (SP) is 80% of the MP.
3. Equation: \(0.80 \times MP = 576\).
4. Solve for MP: \(MP = 576 / 0.80 = 720\).
5. The original Marked Price was $720.
2. A 20% discount means the Selling Price (SP) is 80% of the MP.
3. Equation: \(0.80 \times MP = 576\).
4. Solve for MP: \(MP = 576 / 0.80 = 720\).
5. The original Marked Price was $720.
8.
Find the Selling Price (SP) of a watch marked at $2,000 with successive discounts of 10% and 5%.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Apply the first discount (10%): \(2,000 \times 0.90 = 1,800\).
2. Apply the second discount (5%) on the remaining amount: \(1,800 \times 0.95 = 1,710\).
3. Alternatively, use the multiplier method: \(2,000 \times 0.90 \times 0.95 = 1,710\).
4. The final Selling Price is $1,710.
2. Apply the second discount (5%) on the remaining amount: \(1,800 \times 0.95 = 1,710\).
3. Alternatively, use the multiplier method: \(2,000 \times 0.90 \times 0.95 = 1,710\).
4. The final Selling Price is $1,710.
9.
A dealer marks his goods 20% above the Cost Price (CP) and allows a 10% discount. Find his profit percentage.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let the Cost Price (CP) be 100.
2. The Marked Price (MP) is 20% above CP: \(MP = 100 \times 1.20 = 120\).
3. A 10% discount is given on the MP: \(\text{Discount} = 10\% \text{ of } 120 = 12\).
4. The Selling Price (SP) = \(120 - 12 = 108\).
5. Profit = \(SP - CP = 108 - 100 = 8\).
6. Profit % = \((8 / 100) \times 100 = 8\%\).
2. The Marked Price (MP) is 20% above CP: \(MP = 100 \times 1.20 = 120\).
3. A 10% discount is given on the MP: \(\text{Discount} = 10\% \text{ of } 120 = 12\).
4. The Selling Price (SP) = \(120 - 12 = 108\).
5. Profit = \(SP - CP = 108 - 100 = 8\).
6. Profit % = \((8 / 100) \times 100 = 8\%\).
10.
If the Marked Price is $800 and the Selling Price is $612 after two equal successive discounts, find the discount rate.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let the discount rate be \(d\). The remaining price factor is \((1 - d)\).
2. For two successive discounts: \(800 \times (1 - d)^2 = 612\).
3. \((1 - d)^2 = 612 / 800 = 0.765\).
4. Note: \(612/800 = 306/400 = 153/200 = 76.5/100 = 0.765625\) (more precisely).
5. Take the square root: \(1 - d = \sqrt{0.765625} = 0.875\).
6. \(d = 1 - 0.875 = 0.125\).
7. Convert to percentage: \(0.125 \times 100 = 12.5\%\).
2. For two successive discounts: \(800 \times (1 - d)^2 = 612\).
3. \((1 - d)^2 = 612 / 800 = 0.765\).
4. Note: \(612/800 = 306/400 = 153/200 = 76.5/100 = 0.765625\) (more precisely).
5. Take the square root: \(1 - d = \sqrt{0.765625} = 0.875\).
6. \(d = 1 - 0.875 = 0.125\).
7. Convert to percentage: \(0.125 \times 100 = 12.5\%\).