Discount: Notes और MCQ Practice

आसान भाषा में:

Discount हमेशा Marked Price (MP) यानी अंकित मूल्य पर दिया जाता है। जब कोई Shopkeeper सामान के MP पर छूट देता है, तो मिलने वाला Final Price Selling Price (SP) कहलाता है। सीधा फंडा याद रखिए: Profit/Loss हमेशा CP पर कैलकुलेट होगा और Discount हमेशा MP पर!

Important Formulas:

• Discount = MP − SP
• Discount % = (Discount ÷ MP) × 100
• SP = MP × (100 − Discount %) ÷ 100
• Successive Discount (दो छूट के लिए) = [d1 + d2 − (d1 × d2 ÷ 100)]%
• Golden Ratio Formula (MP और CP का रिश्ता):

MP ÷ CP = (100 + Profit %) ÷ (100 − Discount %)

2 Quick Tricks:

1. Buy x Get y Free Type:

Discount % = [Free Quantity ÷ Total Quantity] × 100

Example: Buy 4 Get 1 Free = [1 ÷ (4 + 1)] × 100 = 20% Discount.

1. Ratio Method for Successive Discount:

अगर Discounts 20% और 12.5% हैं, तो Fraction यूज़ करो:

• 20% = 5 से 4
• 12.5% = 8 से 7

Overall MP to SP = (5 × 8) : (4 × 7) = 40 : 28 = 10 : 7 → यानी 30% Net Discount!

2 Common Mistakes to Avoid:

1. CP पर Discount निकालना: कभी भी Discount को Cost Price पर कैलकुलेट मत करना, Base Value हमेशा MP ही रहेगी।
2. Discounts को सीधा जोड़ना: 20% + 10% Successive Discount कभी 30% नहीं होता! Net discount हमेशा 28% होगा [20 + 10 − (200 ÷ 100)].

1. Concept

In commerce, the Marked Price (MP) is the original price of an item displayed by the seller. The Selling Price (SP) is the actual price at which the item is sold. A Discount is the reduction in the Marked Price. It is always calculated on the Marked Price, not on the Cost Price.

Think of it this way:

• MP: The tag price on the shirt (e.g., ₹1000).
• Discount: The percentage off the tag (e.g., 20% off).
• SP: What you actually pay (₹1000 - 20% of 1000 = ₹800).

The relationship is: SP = MP - Discount Amount.

2. Important Formulas / Rules / Facts

• Discount Amount = MP - SP
• Discount % = (Discount Amount ÷ MP) × 100
• Selling Price (SP) = MP - (Discount % × MP ÷ 100)
• Selling Price (SP) = MP × (100 - Discount %) ÷ 100
• Marked Price (MP) = SP × 100 ÷ (100 - Discount %)
• Cost Price (CP) is not directly used in discount calculations unless Profit/Loss is involved. If Profit/Loss is given, first find SP using CP and Profit/Loss %, then apply discount formulas.

Key Rule: Discount is always on Marked Price (MP), never on Cost Price (CP).

3. Solved Examples

Example 1: Finding Selling Price

Question: The Marked Price of an article is ₹2500. If a discount of 15% is given, what is the Selling Price?

Solution:

1. Formula: SP = MP × (100 - Discount %) ÷ 100
2. Substitute values: SP = 2500 × (100 - 15) ÷ 100
3. SP = 2500 × 85 ÷ 100
4. SP = 25 × 85
5. SP = ₹2125

Answer: The Selling Price is ₹2125.

Example 2: Finding Marked Price

Question: An article is sold for ₹840 after a discount of 20%. What was the Marked Price?

Solution:

1. Formula: MP = SP × 100 ÷ (100 - Discount %)
2. Substitute values: MP = 840 × 100 ÷ (100 - 20)
3. MP = 840 × 100 ÷ 80
4. MP = 840 × (10 ÷ 8)
5. MP = 840 × 1.25
6. MP = ₹1050

Answer: The Marked Price was ₹1050.

Example 3: Finding Discount Percentage

Question: The Marked Price of a book is ₹400. It is sold for ₹320. What is the discount percentage?

Solution:

1. First, find the Discount Amount: Discount = MP - SP
2. Discount = 400 - 320 = ₹80
3. Formula: Discount % = (Discount Amount ÷ MP) × 100
4. Discount % = (80 ÷ 400) × 100
5. Discount % = 0.2 × 100
6. Discount % = 20%

Answer: The discount percentage is 20%.

Example 4: Successive Discounts

Question: A shopkeeper gives a discount of 10% followed by a further discount of 5% on an article with MP ₹2000. What is the final Selling Price?

Solution:

1. First Discount (10%):

• SP1 = 2000 × (100 - 10) ÷ 100
• SP1 = 2000 × 90 ÷ 100 = ₹1800

1. Second Discount (5% on SP1):

• SP2 = 1800 × (100 - 5) ÷ 100
• SP2 = 1800 × 95 ÷ 100
• SP2 = 18 × 95
• SP2 = ₹1710

Answer: The final Selling Price is ₹1710.

Note: Do NOT add 10% + 5% = 15%. Successive discounts are multiplicative, not additive.

Example 5: Discount vs. Profit/Loss

Question: The Cost Price of an item is ₹500. The shopkeeper marks it at 20% above CP and then gives a 10% discount. What is the profit or loss percentage?

Solution:

1. Find MP:

• MP = CP + 20% of CP
• MP = 500 + (20 × 500 ÷ 100) = 500 + 100 = ₹600

1. Find SP (after 10% discount on MP):

• SP = 600 × (100 - 10) ÷ 100
• SP = 600 × 90 ÷ 100 = ₹540

1. Find Profit/Loss:

• Profit = SP - CP = 540 - 500 = ₹40
• Profit % = (Profit ÷ CP) × 100
• Profit % = (40 ÷ 500) × 100 = 8%

Answer: There is a profit of 8%.

4. Shortcuts and Tricks

• Successive Discount Formula: If two successive discounts are d1% and d2%, the equivalent single discount is:

Equivalent Discount % = d1 + d2 - (d1 × d2 ÷ 100)

Example: 10% and 5% discounts are equivalent to 10 + 5 - (50 ÷ 100) = 14.5%.

Use this to quickly find SP: SP = MP × (100 - Equivalent Discount %) ÷ 100.

• Fraction Method: Convert percentages to fractions for faster calculation.
• 10% off = 9/10 of MP
• 20% off = 4/5 of MP
• 25% off = 3/4 of MP
• 50% off = 1/2 of MP

Example: MP ₹800, 25% discount. SP = 800 × 3/4 = ₹600.

• Reverse Calculation Tip: If SP is given and Discount % is known, MP = SP ÷ (1 - Discount %/100).

Example: SP ₹90, 10% discount. MP = 90 ÷ 0.9 = ₹100.

5. Common Mistakes to Avoid

• Mistake 1: Calculating discount on Cost Price (CP) instead of Marked Price (MP). Always use MP.
• Mistake 2: Adding successive discounts (e.g., 10% + 5% = 15%). This is incorrect. Use the equivalent discount formula or calculate step-by-step.
• Mistake 3: Confusing Discount % with Profit/Loss %. Discount is on MP; Profit/Loss is on CP.
• Mistake 4: Forgetting to convert percentages to decimals or fractions correctly. E.g., 15% = 15/100 = 0.15, not 15.
• Mistake 5: In problems involving both markup and discount, failing to first calculate MP from CP before applying the discount.