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?

Difficulty: Easy

15% loss
15% gain
16 2/3% gain
16 2/3% loss
10% loss

Correct Answer: 16 2/3% loss

Explanation:

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:

CP = 630000 / 1.05 = 600000 Result at ₹ 500000 = (500000 − 600000)/600000 * 100 = −100000/600000 * 100 = −1/6 * 100 = −16 2/3% ⇒ 16 2/3% loss

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.

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?

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