Arun purchases 30 kg of wheat at Rs. 11.50 per kg and 20 kg of wheat at Rs. 14.25 per kg. He mixes the two varieties and sells the mixture. At approximately what selling price per kg should he sell the mixture to make a profit of 30%?

Introduction / Context:
This is a mixture and profit problem. Arun buys two different lots of wheat at different prices per kilogram, mixes them, and then sells the mixture at a uniform price. To find the selling price per kg that yields a desired profit percentage, we must first compute the average cost price per kg of the mixture and then apply the profit percentage to this average cost. Such questions are common in competitive exams and test the ability to handle weighted averages and percentage gain together.

Given Data / Assumptions:

• First lot: 30 kg at Rs. 11.50 per kg.
• Second lot: 20 kg at Rs. 14.25 per kg.
• Total quantity after mixing = 30 + 20 = 50 kg.
• Required profit on the mixture = 30%.
• The mixture is sold at a single uniform rate per kg.

Concept / Approach:
We first compute the total cost price of both lots combined. Dividing the total cost by the total quantity gives the average cost price per kg of the mixture. To achieve a 30% profit, the selling price per kg must be 130% of this average cost price, i.e., 1.30 times the average cost. After computing this value, we compare it with the answer options and select the closest approximate value, as the question asks for an approximate price.

Step-by-Step Solution:
Step 1: Cost of first lot = 30 kg * Rs. 11.50/kg = Rs. 345. Step 2: Cost of second lot = 20 kg * Rs. 14.25/kg = Rs. 285. Step 3: Total cost = 345 + 285 = Rs. 630. Step 4: Total quantity = 30 + 20 = 50 kg. Step 5: Average cost price per kg of mixture = total cost / total quantity = 630 / 50 = Rs. 12.60. Step 6: Required selling price per kg to get 30% profit = 1.30 * 12.60. Step 7: Compute 1.30 * 12.60 = 12.60 + 0.30 * 12.60 = 12.60 + 3.78 = Rs. 16.38. Step 8: The nearest option to Rs. 16.38 is Rs. 16.30.

Verification / Alternative check:
If Arun sells the 50 kg mixture at Rs. 16.30 per kg, his total selling price will be approximately 16.30 * 50 = Rs. 815. Total cost is Rs. 630, so profit is about 815 - 630 = Rs. 185. Profit percentage ≈ (185 / 630) * 100 ≈ 29.37%, which is close to 30% and acceptable for an approximate answer. If he sold at Rs. 17.80, the profit percentage would be much higher than 30%, so 16.30 is the best fit among the options.

Why Other Options Are Wrong:
Selling at Rs. 14 or Rs. 15.40 per kg would yield profits far below 30% when compared to the average cost of Rs. 12.60. Selling at Rs. 17.80 or Rs. 15.80 would give profit percentages significantly above 30%. Among the given choices, only Rs. 16.30 per kg approximates the 30% profit requirement based on the computed value of Rs. 16.38.

Common Pitfalls:
Some learners incorrectly average the two buying prices directly without weighting by quantities, or they attempt to apply 30% profit separately on each lot instead of on the mixture. Another common mistake is to miscalculate the total cost or the average cost by forgetting to divide by total quantity. Always compute a weighted average using total cost divided by total quantity before applying the profit percentage.

Final Answer:
Arun should sell the mixture at approximately Rs. 16.30 per kg to earn about 30% profit.