Ram sells goods 25% cheaper than Shyam but 25% dearer than Hari. By what percentage are Hari's goods cheaper than Shyam's?
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A25
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B33 1/3
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C40
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D50
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E20
Answer
Correct Answer: 40
Explanation
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:
0.75S = 1.25H ⇒ S = (1.25/0.75)H = (5/3)H.Hari compared to Shyam: H / S = H / ((5/3)H) = 3/5.Thus Hari's goods are cheaper by (1 − 3/5) * 100% = 2/5 * 100% = 40%.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