Profit and Loss: Notes और MCQ Practice

आसान भाषा में:

जब हम कोई item खरीदते हैं (Cost Price - CP) और उसे बेचते हैं (Selling Price - SP), तो इस transaction में या तो Profit होता है या Loss. SSC CGL में इस topic से direct और indirect questions हमेशा पूछे जाते हैं. बस basic concepts clear रखो और calculation speed तेज़ रखो!

Important Formulas:

• Profit = SP − CP (जब SP > CP)
• Loss = CP − SP (जब CP > SP)
• Profit % = (Profit ÷ CP) × 100
• Loss % = (Loss ÷ CP) × 100
• SP = CP × (100 + Profit %) ÷ 100 [या CP × (100 − Loss %) ÷ 100]
• Discount % = (Discount ÷ Marked Price) × 100 (याद रहे, Discount हमेशा Marked Price (MP) पर मिलता है)

2 Quick Tricks:

1. CP और MP का direct relation: CP ÷ MP = (100 − Discount %) ÷ (100 + Profit %). Direct questions solve करने के लिए यह रामबाण formula है!
2. Successive Discount: अगर d1% और d2% के दो successive discounts दिए हों, तो Single Equivalent Discount = d1 + d2 − (d1 × d2 ÷ 100)%.

2 Common Mistakes (इनसे बचें!):

1. Wrong Base Value: Profit % या Loss % हमेशा CP पर calculate होता है, जब तक question में SP पर calculate करने को न कहा जाए. इसे SP पर calculate करने की भूल न करें.
2. Discount on CP: Discount हमेशा Marked Price (MP) पर calculate होता है, गलती से भी इसे CP पर apply मत करना!

Profit and Loss: Complete Study Notes for SSC CGL

1. Concept

Profit and Loss is one of the most frequently tested topics in the Quantitative Aptitude section of SSC CGL. At its core, the chapter revolves around commercial transactions involving buying, marking, and selling goods.

Key Terms:

• Cost Price (CP): The amount of money spent to purchase, manufacture, or acquire an item (including overhead expenses like transport, repairs, etc.).
• Selling Price (SP): The amount of money received by selling the item.
• Marked Price (MP) or List Price (MRP): The price labeled/printed on the item before offering any concession.
• Profit (Gain): Occurs when an article is sold for more than its cost price (SP > CP).
• Loss: Occurs when an article is sold for less than its cost price (SP < CP).
• Discount: Concession or reduction given on the Marked Price (MP) to arrive at the Selling Price (SP).

Core Rules:

1. Profit or Loss is always calculated on the Cost Price (CP) unless the question explicitly asks for it with respect to the Selling Price.
2. Discount is always calculated on the Marked Price (MP).

2. Important Formulas, Rules, and Facts

Basic Formulas:

• Profit = SP − CP
• Loss = CP − SP
• Profit % = (Profit ÷ CP) × 100
• Loss % = (Loss ÷ CP) × 100

Finding SP and CP Directly:

• When Profit % is given:
• SP = CP × (100 + Profit %) ÷ 100
• CP = (SP × 100) ÷ (100 + Profit %)
• When Loss % is given:
• SP = CP × (100 − Loss %) ÷ 100
• CP = (SP × 100) ÷ (100 − Loss %)

Discount & Marked Price:

• Discount = MP − SP
• Discount % = (Discount ÷ MP) × 100
• SP = MP × (100 − Discount %) ÷ 100
• Relation between MP and CP:
• MP ÷ CP = (100 + Profit %) ÷ (100 − Discount %)
• If there is a loss: MP ÷ CP = (100 − Loss %) ÷ (100 − Discount %)

Successive Discounts:

• If two successive discounts are d1% and d2%, the single equivalent discount is:
• Single Equivalent Discount % = [d1 + d2 − (d1 × d2 ÷ 100)]%

Dishonest Dealer Concepts:

• When a dealer sells at CP but uses false weight:
• Gain % = [Error ÷ (True Value − Error)] × 100
• Alternatively: Gain % = [(True Weight − False Weight) ÷ False Weight] × 100

3. Solved Examples (Exam Style)

Example 1: Basic Profit and Discount

Question: A shopkeeper buys a table for ₹1,200. He marks it 25% above the cost price and allows a discount of 10% on the marked price. Find his net profit and profit percentage.

Solution:

1. Given: CP = ₹1,200
2. Markup = 25% of ₹1,200 = (25 ÷ 100) × 1,200 = ₹300
3. MP = CP + Markup = 1,200 + 300 = ₹1,500
4. Discount = 10% of MP = (10 ÷ 100) × 1,500 = ₹150
5. SP = MP − Discount = 1,500 − 150 = ₹1,350
6. Profit = SP − CP = 1,350 − 1,200 = ₹150
7. Profit % = (Profit ÷ CP) × 100 = (150 ÷ 1,200) × 100 = 12.5%

Example 2: Equal Selling Price with Gain and Loss

Question: A trader sells two radios for ₹1,980 each. On one, he gains 10%, and on the other, he loses 10%. Find his overall gain or loss percentage and the total gain or loss in rupees.

Solution:

1. First radio (Gain of 10%):

• SP1 = ₹1,980
• CP1 = (SP1 × 100) ÷ (100 + 10) = (1,980 × 100) ÷ 110 = ₹1,800

1. Second radio (Loss of 10%):

• SP2 = ₹1,980
• CP2 = (SP2 × 100) ÷ (100 − 10) = (1,980 × 100) ÷ 90 = ₹2,200

1. Total Calculation:

• Total SP = 1,980 + 1,980 = ₹3,960
• Total CP = 1,800 + 2,200 = ₹4,000

1. Total CP > Total SP, therefore overall Loss:

• Net Loss = 4,000 − 3,960 = ₹40
• Loss % = (Loss ÷ Total CP) × 100 = (40 ÷ 4,000) × 100 = 1%

Example 3: Dishonest Shopkeeper

Question: A dishonest merchant claims to sell goods at cost price, but he uses a false weight of 800 grams instead of 1 kilogram (1,000 grams). Find his profit percentage.

Solution:

1. True Weight = 1,000 g
2. Weight actually given = 800 g
3. Error = 1,000 − 800 = 200 g
4. Formula: Gain % = (Error ÷ Actual weight given) × 100
5. Gain % = (200 ÷ 800) × 100 = 25%

Example 4: Relationship Between CP and MP

Question: How much percent above the cost price should a manufacturer mark his goods so that after allowing a discount of 20%, he still earns a profit of 20%?

Solution:

1. Use the direct ratio formula: MP ÷ CP = (100 + Profit %) ÷ (100 − Discount %)
2. MP ÷ CP = (100 + 20) ÷ (100 − 20) = 120 ÷ 80 = 3 ÷ 2
3. Let CP = 2 units, then MP = 3 units
4. Markup = MP − CP = 3 − 2 = 1 unit
5. Markup % = (Markup ÷ CP) × 100 = (1 ÷ 2) × 100 = 50%

• The manufacturer should mark the goods 50% above the cost price.

4. Shortcuts and Tricks

1. The Fraction/Ratio Method

Convert percentages into simple fractions to bypass lengthy algebra:

• 20% Profit = 1 ÷ 5 → CP = 5 units, Profit = 1 unit, SP = 6 units.
• 16.67% Loss = 1 ÷ 6 → CP = 6 units, Loss = 1 unit, SP = 5 units.
• 25% Discount = 1 ÷ 4 → MP = 4 units, Discount = 1 unit, SP = 3 units.

2. Equal SP with Same % Profit and % Loss

When two articles are sold at the same SP, one at a profit of x% and the other at a loss of x%:

• There is always an overall loss.
• Overall Loss % = (x ÷ 10)² % = (x² ÷ 100)%
• (Example: 10% gain and 10% loss on same SP → Net loss = 10² ÷ 100 = 1%)

3. Successive Percentage Change for Net Profit/Loss

If an article is marked up by M% and then discounted by D%:

• Net Profit or Loss % = M − D − [(M × D) ÷ 100]
• A positive result indicates profit; a negative result indicates loss.

4. "Buy X, Get Y Free" Scheme

• Discount % = [Free items ÷ Total items] × 100 = [Y ÷ (X + Y)] × 100
• Example: "Buy 4, Get 1 Free" → Discount % = [1 ÷ (4 + 1)] × 100 = (1 ÷ 5) × 100 = 20%.

5. Common Mistakes to Avoid

1. Base Value Confusion:

• Mistake: Calculating discount on the Cost Price (CP).
• Correction: Discount is always calculated on the Marked Price (MP). Profit/Loss is calculated on the Cost Price (CP).

1. Direct Addition of Discounts:

• Mistake: Assuming that two successive discounts of 20% and 10% equal 30%.
• Correction: Successive discounts compound. The equivalent discount is 20 + 10 − [(20 × 10) ÷ 100] = 30 − 2 = 28%.

1. Confusing Same CP vs. Same SP:

• If two items have the same CP, one sold at x% profit and another at x% loss, the net outcome is No Profit, No Loss.
• If two items have the same SP, one sold at x% profit and another at x% loss, the net outcome is always a Loss of (x² ÷ 100)%.

1. Dishonest Weight Ratio Inversion:

• Mistake: Computing Gain % as (200 ÷ 1,000) × 100 when 800 g is given instead of 1,000 g.
• Correction: The base for the merchant is the quantity he actually dispensed (800 g), not the nominal weight (1,000 g). Correct calculation is (200 ÷ 800) × 100 = 25%.