Two-thirds of a consignment is sold at a profit of 5% and the remainder at a loss of 2%. If the total profit is Rs 400, find the value (cost) of the entire consignment.

Introduction:
When parts of a lot are sold at different percentages of gain or loss, the overall profit equals the weighted sum of those percentages applied to the corresponding cost portions. Here, the weights are two-thirds and one-third of total cost.

Given Data / Assumptions:

• Fraction sold at profit 5%: 2/3 of total cost
• Fraction sold at loss 2%: 1/3 of total cost
• Total profit = Rs 400; Let total cost = C

Concept / Approach:
Overall profit = (2/3 * 5% * C) + (1/3 * −2% * C) = C * (0.05 * 2/3 − 0.02 * 1/3). Solve for C using the given absolute profit of Rs 400.

Step-by-Step Solution:
Profit = C * (0.10/3 − 0.02/3) = C * (0.08/3)So 400 = C * (0.08/3) ⇒ C = 400 * 3 / 0.08C = 1200 / 0.08 = 15000

Verification / Alternative check:
Two-thirds of 15000 is 10000; 5% of that is 500. One-third is 5000; 2% loss is 100. Net profit = 500 − 100 = 400 (matches).

Why Other Options Are Wrong:
20000, 10000, 12000: Their weighted gains/losses do not produce Rs 400.

Common Pitfalls:
Applying percentages to selling price instead of cost; forgetting that the weights (2/3 and 1/3) apply to cost portions, not counts unless unit costs are uniform.

Final Answer:
15000