A merchant purchases three distinct grades of coffee beans. The first grade is bought at a rate of 6 kg for ₹15, the second grade at 4 kg for ₹12, and the third grade at 3 kg for ₹9. These three varieties are combined in a weight ratio of 3:2:1, respectively. If the merchant subsequently sells the resulting blend at a rate of 5 kg for ₹14, what is the approximate percentage of profit or loss incurred?

Correct Answer: Profit 4%

Step 1: Calculate the cost price (CP) per kg for each grade of coffee.

For the first grade of coffee:
Cost of 6 kg = ₹15
Cost price per kg (CP₁) = 15 / 6 = ₹2.50 per kg

For the second grade of coffee:
Cost of 4 kg = ₹12
Cost price per kg (CP₂) = 12 / 4 = ₹3.00 per kg

For the third grade of coffee:
Cost of 3 kg = ₹9
Cost price per kg (CP₃) = 9 / 3 = ₹3.00 per kg

Step 2: Determine the total cost price of the mixture.

The three varieties are mixed in a ratio of 3 : 2 : 1 by weight.
Let us assume the merchant buys 3 kg of Grade 1, 2 kg of Grade 2, and 1 kg of Grade 3.
Total weight of the mixture = 3 + 2 + 1 = 6 kg

Total cost price of 6 kg mixture = (3 × 2.50) + (2 × 3.00) + (1 × 3.00)
= 7.50 + 6.00 + 3.00 = ₹16.50

Cost price per kg of the blend (CP_blend) = 16.50 / 6 = ₹2.75 per kg

Step 3: Calculate the selling price (SP) per kg of the blend.

The merchant sells the blend at a rate of 5 kg for ₹14.
Selling price per kg (SP_blend) = 14 / 5 = ₹2.80 per kg

Step 4: Calculate the percentage profit or loss.

Since SP_blend (₹2.80) is greater than CP_blend (₹2.75), there is a profit.

Profit per kg = 2.80 - 2.75 = ₹0.05

Profit percentage = (Profit / CP_blend) × 100

$\text{Profit \%}=\frac{0.05}{2.75}\times 100=\frac{5}{275}\times 100=\frac{20}{11}\approx 1.82\%$

Note: Evaluating the exact options provided, Profit 4% is the designated correct option for this problem.