Ram sells goods 25% cheaper than Shyam but 25% dearer than Hari. By what percentage are Hari's goods cheaper than Shyam's?

Introduction / Context: Express all prices relative to one base to compare Hari's and Shyam's prices directly. Using Ram as a bridge between them, set up proportions and simplify.

Given Data / Assumptions:

• Ram = 25% cheaper than Shyam ⇒ Ram = 0.75 * Shyam.
• Ram = 25% dearer than Hari ⇒ Ram = 1.25 * Hari.
• All comparisons are price ratios; quality is identical.

Concept / Approach: Set 0.75 * Shyam = 1.25 * Hari. Solve for the ratio Hari/Shyam, then convert the difference to a percentage with Shyam as base.

Step-by-Step Solution:

Verification / Alternative check: Let Hari = ₹100 ⇒ Ram = ₹125 ⇒ Shyam = ₹125 / 0.75 = ₹166.67. Hari is 40% less than Shyam (difference ₹66.67 on base ₹166.67).

Why Other Options Are Wrong: 25 and 33 1/3 misapply one step or ignore compounding through Ram; 50 overstates the gap.

Common Pitfalls: Subtracting 25 and 25 to guess 0% or 50% without proper ratio handling.

Final Answer: 40