Overall 4% loss by splitting sales: A merchant has 160 kg of goods. He sells some at a 10% profit and the rest at a 6% loss. If his overall result is a 4% loss, how many kilograms were sold at a 6% loss?

Introduction / Context:We apply weighted-average gain/loss on quantities. By assigning a unit cost for simplicity, the overall revenue condition leads directly to the split between the two sale categories.

Given Data / Assumptions:

• Total quantity = 160 kg.
• Profit on part = 10%; loss on remainder = 6%.
• Overall loss = 4%.

Concept / Approach:Let x kg be sold at 10% profit and (160 − x) kg at 6% loss. With a notional cost price (CP) of ₹ 1 per kg, compute the total revenue and match it to the overall 4% loss target (i.e., 0.96 of total CP). Solve for x and then obtain the loss quantity (160 − x).

Step-by-Step Solution:Revenue = 1.10x + 0.94(160 − x) = 0.16x + 150.4.Overall revenue = 0.96 × 160 = 153.6.0.16x + 150.4 = 153.6 ⇒ 0.16x = 3.2 ⇒ x = 20.Therefore, sold at 6% loss = 160 − 20 = 140 kg.

Verification / Alternative check:Check: Profit portion revenue = 1.10 × 20 = 22; loss portion revenue = 0.94 × 140 = 131.6. Total = 153.6 = 0.96 × 160, matching 4% loss overall.

Why Other Options Are Wrong:

• 120, 150, and 160 kg do not simultaneously satisfy the overall 4% loss condition with the given rates.

Common Pitfalls:

• Equating the average of 10% and −6% to −4% (simple averaging is invalid without weighting by quantities).

Final Answer:140 kgs