Profit and Loss — A house sold for ₹ 630000 yields a 5% profit. If instead it had been sold for ₹ 500000, what would have been the percentage result: profit or loss?

Introduction / Context: First recover the true cost price (CP) from a sale that produced 5% profit. Then evaluate the hypothetical sale price against CP to determine the profit or loss percentage in the alternate scenario.

Given Data / Assumptions:

• SP_actual = ₹ 630000 at +5% profit ⇒ SP = 1.05 * CP.
• Hypothetical SP_alt = ₹ 500000.

Concept / Approach: Compute CP = SP_actual / 1.05. Then compute percentage result at SP_alt using (SP_alt − CP)/CP * 100 and classify as profit or loss by the sign.

Step-by-Step Solution:

Verification / Alternative check: Profit at 630000: (630000 − 600000)/600000 * 100 = 5% (matches the premise).

Why Other Options Are Wrong: 15% loss/gain and 10% loss are inconsistent with the exact 1/6 ratio; 16 2/3% gain has the wrong sign.

Common Pitfalls: Treating 630000 to 500000 as a 130000 drop over the selling price base, rather than evaluating against the cost base for profit/loss percentage.

Final Answer: 16 2/3% loss