Unit pricing with gain → recover buying rate per dozen A vendor sells lemons at a rate of 5 for ₹14 and earns a 40% profit on this selling rate. At what total price did he buy 1 dozen (12) lemons?

Introduction / Context:
This is a classic profit-and-loss unit-rate question. We are told the seller makes a 40% profit when selling lemons at a quoted “x for ₹y” rate. From the selling rate (per lemon) and the gain percentage, we can reverse-calculate the true cost per lemon and then scale to a dozen.

Given Data / Assumptions:

• Selling rate: 5 lemons for ₹14.
• Profit rate on cost: 40%.
• Find: total cost for 12 lemons (1 dozen).
• Assume identical quality and uniform cost per lemon.

Concept / Approach:
Compute the selling price per lemon, then divide by (1 + gain%) to get the cost price per lemon. Finally multiply the per-lemon cost by 12 to get the cost of a dozen.

Step-by-Step Solution:
SP per lemon = 14 / 5 = ₹2.80.Gain% = 40% ⇒ SP = 1.40 * CP ⇒ CP per lemon = 2.80 / 1.40 = ₹2.00.Cost for 12 lemons = 12 * 2.00 = ₹24.

Verification / Alternative check:
If CP per lemon is ₹2, then for 5 lemons CP = ₹10, SP = ₹14, profit = ₹4, which is 40% of ₹10. This confirms the backward calculation.

Why Other Options Are Wrong:
₹20 underestimates because it treats the profit as lower than 40%.₹21 and ₹26 do not align with 2.80 / 1.40 = 2.00 per lemon.₹28 corresponds to a higher per-lemon cost than allowed by a 40% margin at the given SP.

Common Pitfalls:
Applying 40% to the selling price instead of the cost price, or scaling the “5 for ₹14” rate directly to a dozen without removing the profit first.

Final Answer:
₹ 24