How much chicory at Rs. 24 per kg must be added to 15 kg of tea priced at Rs. 60 per kg so that the resulting mixture is worth Rs. 39 per kg?

Introduction / Context:
We blend a cheaper component (chicory) with a dearer one (tea) to achieve a target price. Set up the value equation: total cost divided by total weight equals the target price.

Given Data / Assumptions:

• Tea: 15 kg at Rs. 60/kg.
• Chicory: x kg at Rs. 24/kg.
• Mixture price: Rs. 39/kg.

Concept / Approach:
Use (total cost)/(total weight) = target price. Solve for x.

Step-by-Step Solution:
Total cost = 15*60 + 24x = 900 + 24xTotal weight = 15 + x(900 + 24x)/(15 + x) = 39900 + 24x = 585 + 39x ⇒ 315 = 15x ⇒ x = 21 kg

Verification / Alternative check:
Alligation: 60 to 39 (diff 21) and 39 to 24 (diff 15) gives ratio tea : chicory = 15 : 21 = 5 : 7. For tea 15 kg, chicory = 15*(7/5) = 21 kg.

Why Other Options Are Wrong:
Other values of x do not satisfy the price equation exactly.

Common Pitfalls:
Mixing up which side of alligation corresponds to which quantity; use inverse differences.

Final Answer:
21 kg