By mixing two qualities of pulses in the ratio 2 : 3 and selling the mixture at Rs. 22 per kilogram, a shopkeeper makes a profit of 10%. If the cost price of the cheaper quality is Rs. 14 per kilogram, what is the cost price per kilogram of the dearer (more expensive) quality?

Introduction / Context:
This question combines mixture and profit concepts. Two types of pulses with different cost prices are mixed in a given ratio and sold at a single price per kilogram with a known profit percentage. The goal is to determine the cost price of the more expensive quality using an average cost and profit relationship.

Given Data / Assumptions:

• Two qualities of pulses are mixed in the ratio 2 : 3 (cheaper : dearer).
• Selling price of the mixture = Rs. 22 per kg.
• Profit on the mixture = 10%.
• Cost price of the cheaper quality = Rs. 14 per kg.
• We must find the cost price of the dearer quality.

Concept / Approach:
Let the cost price of the dearer pulses be x rupees per kg. For every 2 kg of cheaper pulses at Rs. 14 per kg and 3 kg of dearer pulses at Rs. x per kg, total cost and total quantity can be computed. The cost per kg of the mixture is then the total cost divided by 5 kg. Since the shopkeeper makes a 10% profit when selling at Rs. 22, the cost per kg must be 22 / 1.10. Setting this equal to the weighted average cost leads to an equation in x.

Step-by-Step Solution:
Step 1: Let the dearer pulses cost x rupees per kg.Step 2: Cost of 2 kg cheaper pulses = 2 * 14 = Rs. 28.Step 3: Cost of 3 kg dearer pulses = 3x rupees.Step 4: Total cost for 5 kg mixture = 28 + 3x.Step 5: Cost price per kg of mixture = (28 + 3x) / 5.Step 6: Selling price per kg = Rs. 22 with 10% profit, so cost price per kg = 22 / 1.10 = Rs. 20.Step 7: Set weighted average cost equal to 20: (28 + 3x) / 5 = 20.Step 8: Multiply both sides by 5: 28 + 3x = 100, so 3x = 72 and x = 24.

Verification / Alternative check:
With cheaper pulses at Rs. 14 and dearer at Rs. 24, cost for 2 kg cheaper = 28, for 3 kg dearer = 72, total = 100.Total quantity = 5 kg, so cost per kg = 100 / 5 = Rs. 20.Selling price per kg = Rs. 22, giving profit = 2 rupees per kg, or 2 / 20 * 100 = 10%.

Why Other Options Are Wrong:
At Rs. 23, weighted average cost would not equal Rs. 20. Rs. 25 would raise the average cost above 20, reducing profit percentage below 10 or eliminating profit altogether. Rs. 21 also fails to produce the correct 10% profit when the mixture is sold at Rs. 22. Therefore those values cannot be correct, and “None of these” is unnecessary since Rs. 24 is a direct match.

Common Pitfalls:
Some learners confuse the ratio 2 : 3 as a price ratio rather than a quantity ratio, or they treat 10% profit as a simple addition of Rs. 2 without verifying the base. Others may inadvertently use selling price instead of cost price when forming the average. Writing the total cost and total quantity explicitly, then linking to the required cost per kg, keeps the logic clear.

Final Answer:
The cost price of the dearer quality of pulses is Rs. 24 per kg.