Ram sells his goods 25% cheaper than Shyam and 25% dearer than Bram. By what percentage are Bram's goods cheaper than Shyam's goods?

Introduction / Context:
This percentage problem compares the prices of goods sold by three people, Ram, Shyam, and Bram. It checks your ability to handle successive percentage changes and to compare prices expressed in relative terms rather than absolute values. Such questions are very common in profit and loss sections of aptitude exams and help build comfort with chained percentage relationships between different entities.

Given Data / Assumptions:

• Ram sells his goods 25% cheaper than Shyam.
• Ram sells his goods 25% dearer (more expensive) than Bram.
• We are asked to find how much percent Bram's goods are cheaper than Shyam's goods.
• There is no mention of actual rupee values, so we can assume a convenient base price for Shyam to simplify calculations.

Concept / Approach:
When dealing with percentage comparisons, it is helpful to assume a simple base value. Here, we can assume Shyam's price is 100 units. Ram sells 25% cheaper than Shyam, so his price is 75 units. The statement that Ram is 25% dearer than Bram means Ram's price is 125% of Bram's price. Using that relation, we can compute Bram's price and then compare Bram's price to Shyam's price to find the required percentage difference. The key concepts used are basic percentage calculations and relative comparison.

Step-by-Step Solution:
Step 1: Assume Shyam's price is 100 units.Step 2: Since Ram sells 25% cheaper than Shyam, Ram's price is 100 - 25% of 100 = 100 - 25 = 75 units.Step 3: Ram sells 25% dearer than Bram, so Ram's price is 125% of Bram's price.Step 4: Let Bram's price be B. Then 1.25 * B = 75, because Ram's price is 75 units.Step 5: Solve for B: B = 75 / 1.25 = 60 units.Step 6: Now Shyam's price is 100 units and Bram's price is 60 units. The reduction from Shyam to Bram is 100 - 60 = 40 units.Step 7: Express this difference as a percentage of Shyam's price: (40 / 100) * 100% = 40%.

Verification / Alternative check:
We can verify by checking all relationships again. Starting with Shyam = 100 units, Bram = 60 units is 40% cheaper than Shyam because 40% of 100 is 40. Ram, being 25% dearer than Bram, should be 60 + 25% of 60 = 60 + 15 = 75 units. This also matches the earlier condition that Ram is 25% cheaper than Shyam, because 25% of 100 is 25 and 100 - 25 = 75. Both relationships hold, so the calculation is consistent and correct.

Why Other Options Are Wrong:
Option 60% would mean Bram sells at only 40 units when Shyam is at 100, which would not satisfy the given 25% dearer relationship with Ram. Option 50% would make Bram's price 50 units and would not produce Ram's price as both 75 and 25% dearer than Bram. Option 30% would give Bram's price as 70 units, making Ram's price inconsistent with the described percentage relations. Option 20% is clearly too small as Bram's price would be 80 units and Ram's price could not be both 75 and 25% cheaper than Shyam. Therefore, 40% is the only consistent answer.

Common Pitfalls:
A typical mistake is to directly add or subtract percentages without understanding which person is the reference base. Some learners also treat the 25% cheaper and 25% dearer statements as symmetrical, which is not correct because the percentage is applied on different bases. Another error is to compare Bram and Shyam via Ram in a single step without using algebra, which often leads to numerical slips. Always fix one person's price as 100 and trace the relationships carefully through each comparison.

Final Answer:
Bram's goods are 40% cheaper than Shyam's goods.