Profit and Loss – Two horses sold at equal selling prices, no overall gain or loss: A man sells two horses for Rs 4000 each and reports neither a profit nor a loss overall. If one horse is sold at a 25% gain, then at what percentage loss is the other horse sold so that the combined transaction breaks even?

Introduction / Context:
This question tests the classic “equal selling price with opposite outcomes” idea. When two items are sold at the same selling price, a gain on one item and a loss on the other do not cancel arithmetically; the relationship must be computed from actual cost and selling price values.

Given Data / Assumptions:

• Selling price of horse 1 = Rs 4000
• Selling price of horse 2 = Rs 4000
• Gain on horse 1 = 25%
• Overall result on both horses together = no profit, no loss

Concept / Approach:
Compute the cost of the first horse from its gain. Then use the zero overall profit condition to find the cost of the second horse. Finally compute the percentage loss on the second horse using loss% = (CP − SP) / CP * 100.

Step-by-Step Solution:
CP1 = SP1 / 1.25 = 4000 / 1.25 = 3200Total SP of both horses = 4000 + 4000 = 8000Zero overall profit ⇒ Total CP must also be 8000Therefore CP2 = 8000 − 3200 = 4800Loss% on horse 2 = (4800 − 4000) / 4800 * 100 = 800 / 4800 * 100 = 16.666...% = 16 2/3%

Verification / Alternative check:
Using the identity for equal selling prices with +a% and −b% does not directly apply unless CPs are the same. Here, computing CPs ensures accuracy and confirms 16 2/3%.

Why Other Options Are Wrong:
18 2/9% and 25% are larger than required; 14 2/7% is smaller. “None” is incorrect because 16 2/3% matches the derived value.

Common Pitfalls:
Taking average of +25% and −x% to get zero, which is wrong with equal SP. Always compute using CP or SP relationships.

Final Answer:
16 2/3%