Profit and Loss with Dishonest Seller Questions – Concepts, Formulas, SSC Important Questions

📘 Part 1: Basic Profit and Loss Formulas:-

Understanding Profit and Loss is essential for all government job aspirants. Here are the most important concepts and formulas:

✅ Key Terms:

• Cost Price (CP): Price at which the article is bought
• Selling Price (SP): Price at which the article is sold
• Profit or Gain: When SP > CP
• Loss: When CP > SP
• Marked Price (MP): The listed price before any discount
• Discount: A reduction on Marked Price

✅ Basic Formulas:

🧠 Part 2: Dishonest Seller – Concept and Formulas:-

The topic of dishonest seller questions frequently appears in SSC, Railway, and Banking exams. A dishonest seller uses false weights or adulteration to earn more profit.

✅ Concepts of Dishonest Seller:

1. Selling at Cost Price but using False Weight:
   A seller claims to sell at CP but uses less weight than 1 kg, for example, 950 gm instead of 1000 gm. This leads to hidden profit.
2. Mixing Cheap Articles (Adulteration):
   A dishonest seller mixes cheaper items with costlier ones and sells the mixture at the price of the costlier item.

✅ Dishonest Seller Formulas:

🔹 Profit % when using false weight:

Profit % = [(Actual Weight – Used Weight) / Used Weight] × 100

This formula helps you calculate the hidden profit when a seller uses less weight than claimed.

🔹 False Weight Used:

If profit percentage and actual weight are known, then:

Used Weight = Actual Weight / [1 + (Profit % / 100)]

This formula helps find how much weight the seller actually used to make a certain profit.

🔹 Adulteration or Mixing Formula:

Overall Cost Price (CP) = [(x × CP1) + (y × CP2)] / (x + y)

Where:

• x = quantity of item 1
• y = quantity of item 2
• CP1 = cost price of item 1
• CP2 = cost price of item 2

This is used when a seller mixes two items of different prices to create a profitable mixture.

📝 Part 3: Important Solved Dishonest Seller Questions:-

Q1) A dishonest shopkeeper claims to sell sugar at cost price but uses a weight of 950 gm instead of 1 kg. Find his profit percentage.

Solution:
Actual weight = 1000 gm, Used weight = 950 gm
Profit % = (1000 – 950)/950 × 100 = 5.26%

Q2) A shopkeeper mixes 2 kg of rice costing ₹40/kg with 3 kg of rice costing ₹30/kg and sells the mixture at ₹42/kg. Find his profit percentage.

Solution:
Total Cost = (2×40) + (3×30) = 80 + 90 = 170
Total Quantity = 5 kg
CP/kg = 170/5 = 34
SP = ₹42
Profit% = (42 – 34)/34 × 100 = 23.53%

Q3) A dishonest seller uses a weight of 800 gm instead of 1 kg and sells at cost price. Find his profit percentage.

Solution:
Profit % = (1000 – 800)/800 × 100 = 25%

Q4) A shopkeeper mixes 5 kg of ghee costing ₹90/kg with 3 kg costing ₹60/kg and sells the mixture at ₹84/kg. Find his profit percentage.

Solution:
Total Cost = (5×90) + (3×60) = 450 + 180 = ₹630
Total Quantity = 8 kg
CP/kg = 630/8 = ₹78.75
Profit % = (84 – 78.75)/78.75 × 100 ≈ 6.66%

Q5) A dishonest trader uses 960 gm in place of 1 kg and still claims to sell at cost price. Find his profit %.

Solution:
Profit % = (1000 – 960)/960 × 100 = 40/960 × 100 = 4.17%

Q6) A dishonest dealer sells goods at 10% profit and also uses weights 10% less than the actual. What is the total gain percentage?

Solution:
Let CP = ₹100, then SP = ₹110
But weight is 90% of 1 kg
Profit % = (110 – 90)/90 × 100 = 20/90 × 100 = 22.22%

Q7) A trader claims to sell at CP but uses 900 gm in place of 1 kg. Find profit %.

Solution:
Profit % = (1000 – 900)/900 × 100 = 11.11%

Q8) A seller mixes 4 kg sugar at ₹45/kg with 6 kg sugar at ₹25/kg and sells the mixture at ₹40/kg. What is the gain %?

Solution:
Total CP = (4×45) + (6×25) = 180 + 150 = ₹330
Total kg = 10
CP/kg = 330/10 = ₹33
Profit % = (40 – 33)/33 × 100 = 21.21%

Q9) A dishonest milkman mixes 2 liters of water (free) with 8 liters of milk costing ₹50/liter and sells the entire at ₹55/liter. Find profit %.

Solution:
Cost of 8L milk = 8×50 = ₹400
Total quantity = 10L
SP = 10×55 = ₹550
Profit = 550 – 400 = ₹150
Profit % = 150/400 × 100 = 37.5%

Q10) A trader mixes 5 kg of wheat costing ₹25/kg with 5 kg of wheat costing ₹35/kg and sells the mixture at ₹34/kg. Find gain %.

Solution:
Total CP = (5×25) + (5×35) = 125 + 175 = ₹300
Total kg = 10
CP/kg = 300/10 = ₹30
Profit % = (34 – 30)/30 × 100 = 13.33%

🧪 Part 4: Practice Dishonest Seller Questions:-

Test your learning with these practice questions. Answers provided below.

Practice Questions:

Q1) A dishonest shopkeeper uses a weight of 900 gm instead of 1 kg. What is his gain %?

Q2) A seller adds 2 kg of sand (free) to 8 kg of salt costing ₹60/kg and sells the whole mixture at ₹66/kg. What is the profit %?

Q3) A dishonest milkman mixes 3 liters of water in 9 liters of milk costing ₹50/liter and sells the mixture at ₹55/liter. Find his profit %.

Q4) A trader claims to sell at cost price but uses 920 gm in place of 1 kg. Find his profit percentage.

Q5) A shopkeeper mixes 2 kg of sugar at ₹50/kg and 3 kg at ₹40/kg and sells at ₹52/kg. What is the gain percentage?

✅ Answers:

1. 11.11%
2. 25%
3. 41.66%
4. 8.69%
5. 13.33%

🔚 Conclusion:

Understanding profit and loss basics along with mastering dishonest seller questions is crucial for competitive exams like SSC, Railways, and Banking. These questions are not only scoring but often repeated with slight variations. Practice well using the formulas and examples provided.

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