Two equal selling prices: one house at +20%, the other at −20% A man sells two houses for ₹96,000 each. On the first he makes a 20% profit; on the second he incurs a 20% loss. What is the overall percentage result?

Introduction / Context:Equal selling prices with opposite percentages do not cancel because the cost bases differ. We compute cost for each, sum, and compare with the total selling amount to get the net percentage.

Given Data / Assumptions:

• Both SPs = ₹96,000.
• First: +20% profit; Second: −20% loss.

Concept / Approach:CP_1 = 96,000 / 1.20; CP_2 = 96,000 / 0.80. Net = (SP_1 + SP_2) − (CP_1 + CP_2). Percentage = Net / (CP_1 + CP_2) * 100.

Step-by-Step Solution:CP_1 = ₹80,000; CP_2 = ₹120,000.Total CP = ₹200,000; Total SP = ₹192,000.Net = 192,000 − 200,000 = −₹8,000 ⇒ Loss% = 8,000/200,000 * 100 = 4% loss.

Verification / Alternative check:Relative base logic: the loss operates on the larger base (₹120,000) and outweighs the gain on the smaller base (₹80,000), producing a net loss.

Why Other Options Are Wrong:6% or 4% gain contradict the numeric totals; 'no profit, no loss' ignores base dependence; 6% loss is too large.

Common Pitfalls:Adding +20 and −20 as if they cancel; percentages are multiplicative and base-dependent.

Final Answer:4% loss