Question 1

A shopkeeper claims to sell goods at cost price but uses a false weight of 900 g instead of 1 kg. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives only 900 g but charges for 1000 g (1 kg). Step 2: Profit = 1000 - 900 = 100 g on every 900 g given. Step 3: Profit % = (Error / True Value - Error) × 100 = (100 / 900) × 100 = 100/9 = 11.11%. Therefore, answer is 11 1/9%.

Question 2

A shopkeeper buys a table for ₹800 and sells it for ₹1,040. What is his profit percentage?

Accepted Answer

Step 1: Identify Cost Price (CP) = ₹800 and Selling Price (SP) = ₹1,040
Step 2: Calculate Profit = SP − CP = 1,040 − 800 = ₹240
Step 3: Apply Profit % formula = (Profit / CP) × 100
Step 4: Profit % = (240 / 800) × 100 = 0.30 × 100 = 30%
Therefore, the profit percentage is 30%.

Question 3

A shopkeeper marks his goods 25% above the cost price and offers a discount of 10%. What is his profit percentage?

Accepted Answer

Step 1: Let Cost Price (CP) = ₹100. Step 2: Marked Price (MP) = 100 + 25% of 100 = ₹125. Step 3: Selling Price (SP) after 10% discount = 125 − 10% of 125 = 125 − 12.50 = ₹112.50. Step 4: Profit = SP − CP = 112.50 − 100 = ₹12.50. Step 5: Profit% = (12.50/100) × 100 = 12.5%. Therefore, the profit percentage is 12.5%.

Question 4

A shopkeeper buys 120 pens at ₹8 per pen. He sells 80 pens at ₹12 per pen and the remaining pens at ₹10 per pen. What is his overall profit percentage?

Accepted Answer

Step 1: Calculate Cost Price (CP). CP = 120 × ₹8 = ₹960. Step 2: Calculate Selling Price (SP) for 80 pens at ₹12 each. SP₁ = 80 × ₹12 = ₹960. Step 3: Calculate SP for remaining 40 pens at ₹10 each. SP₂ = 40 × ₹10 = ₹400. Step 4: Total SP = ₹960 + ₹400 = ₹1360. Step 5: Profit = SP - CP = ₹1360 - ₹960 = ₹400. Step 6: Profit % = (Profit / CP) × 100 = (400 / 960) × 100 = 41.67% ≈ 41⅔% or 125/3 %. This equals approximately 41.67%, which rounds to 41⅔% in fractional form or 125/3 %.

Question 5

A shopkeeper marks an article at ₹1,200. He offers a discount of 15% on the marked price. However, he still makes a profit of 20% on the cost price. What is the cost price of the article?

Accepted Answer

Step 1: Calculate Selling Price (SP) after 15% discount on MP of ₹1,200.
Discount = 15% of 1,200 = 0.15 × 1,200 = ₹180
SP = MP − Discount = 1,200 − 180 = ₹1,020

Step 2: Use Profit formula to find Cost Price (CP).
Profit = 20% means SP = CP × (1 + 20/100) = CP × 1.20
1,020 = CP × 1.20
CP = 1,020 ÷ 1.20 = ₹850

Step 3: Verify: Profit = SP − CP = 1,020 − 850 = ₹170
Profit% = (170/850) × 100 = 20% ✓

Therefore, the cost price is ₹850.

Question 6

A dishonest shopkeeper claims to sell goods at cost price, but uses false weights. He gives only 800 grams when he should give 1000 grams for every kilogram sold. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper claims to sell at cost price, meaning Selling Price = Cost Price (per unit weight claimed).

Step 2: He gives 800 g but charges for 1000 g. This means:
- Cost incurred by shopkeeper = 800 g at cost price
- Revenue received = Price of 1000 g at cost price (since he claims to sell at CP)

Step 3: Let cost price per gram = C
- Actual Cost = 800C
- Selling Price = 1000C (he charges the price for 1000 g)

Step 4: Profit = SP - CP = 1000C - 800C = 200C

Step 5: Profit % = (Profit / CP) × 100
Profit % = (200C / 800C) × 100
Profit % = (200/800) × 100
Profit % = (1/4) × 100
Profit % = 25%

Therefore, the profit percentage is 25%.

Question 7

A shopkeeper marks his goods 40% above cost price and offers a discount of 20% on the marked price. He also gives one article free on purchase of every 4 articles. Find the overall profit or loss percentage.

Accepted Answer

Step 1: Let CP of each article = 100. So CP of 4 articles = 400. Step 2: MP of each article = 140 (40% above CP). MP of 4 articles = 560. Step 3: After 20% discount on MP: SP of 4 articles = 560 × 0.80 = 448. Step 4: But customer gets 5 articles (4 + 1 free), so actual CP = 5 × 100 = 500. Step 5: Profit/Loss% = (448 - 500)/500 × 100 = -52/500 × 100 = -10.4%. Therefore, the shopkeeper incurs a loss of 10.4%.

Question 8

A trader marks his goods 40% above the cost price and offers a discount of 20% on the marked price. Due to a faulty weighing machine, he gives only 800 g instead of 1000 g. What is his overall profit percentage?

Accepted Answer

Step 1: Let CP per 1000 g = 100. Marked Price = 140. After 20% discount, SP = 140 × 0.8 = 112. Step 2: But he gives only 800 g. So effective CP for 800 g = 80 (since CP of 1000 g = 100). Step 3: Profit % = [(112 − 80) / 80] × 100 = (32/80) × 100 = 40%. Therefore, answer is 40%.

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