A shopkeeper gives a discount of 12% on the purchase of 10 kg of sugar. The cost price of the sugar is ₹30/kg, and the marked price is ₹38/kg. The weighing machine of the shopkeeper is faulty, and it shows weight of 1 kg when the actual weight is 900 grams. Find the percentage profit of the shop keeper (rounded off to two decimal places).

Given:

Cost price (CP) of sugar = ₹30/kg

Marked price (MP) of sugar = ₹38/kg

Discount = 12%

Faulty weight = 1 kg (actual weight is 900 grams)

Formula Used:

1. Selling Price (SP) after discount = MP × (1 - Discount%)

2. Actual weight sold = Faulty weight × weight sold according to faulty machine

3. Total SP = SP × weight sold according to faulty machine

4. Profit% = [(Total SP - Total CP) / Total CP] × 100

Calculation:

1. Calculate SP after discount:

Discount = 12%

⇒ SP = MP × (1 - Discount%)

⇒ SP = 38 × (1 - 0.12)

⇒ SP = 38 × 0.88

⇒ SP = 33.44 ₹/kg

2. Calculate actual weight sold for 10 kg:

Faulty weight for 1 kg = 900 g or 900/1000 kg

Actual weight = 10 kg × 0.9 kg

⇒ Actual weight = 9 kg

3. Calculate total SP:

Total SP = SP × weight sold according to faulty machine

⇒ Total SP = 33.44 × 10

⇒ Total SP = 334.4 ₹

4. Calculate total CP:

Total CP = CP × Actual weight

⇒ Total CP = 30 × 9

⇒ Total CP = 270 ₹

5. Calculate Profit%:

Profit% = [(Total SP - Total CP) / Total CP] × 100

⇒ Profit% = [(334.4 - 270) / 270] × 100

⇒ Profit% = (64.4/ 270) × 100

⇒ Profit% ≈ 23.85%

The percentage profit of the shopkeeper is approximately 23.85%.