Price drop and quantity gained: A 20% reduction in the price of wheat allows a buyer to purchase 3.5 kg more for a fixed budget of ₹770. What was the original price per kilogram (₹/kg)?

Introduction / Context:
This percentage-and-proportion problem asks you to convert a stated percentage reduction in price into an equivalent increase in quantity for a fixed budget. By linking price and quantity through the identity Money = Price * Quantity, we can solve for the original price per kilogram.

Given Data / Assumptions:

• Budget is fixed at ₹770.
• Price of wheat is reduced by 20% (new price = 80% of old price).
• Due to the reduction, the buyer gets 3.5 kg more than before.
• No other discounts or taxes are involved.

Concept / Approach:
Let the original price be p (₹/kg). Then original quantity = 770 / p. New price = 0.8 * p, so new quantity = 770 / (0.8p) = (770/p) / 0.8 = 1.25 * (770/p). The difference between new and old quantities equals 3.5 kg. Solve for p directly.

Step-by-Step Solution:
Original qty = 770 / pNew qty = 770 / (0.8p) = 1.25 * (770 / p)Increase in qty = (1.25 − 1) * (770 / p) = 0.25 * (770 / p)0.25 * (770 / p) = 3.5 ⇒ 770 / p = 14 ⇒ p = 770 / 14 = 55

Verification / Alternative check:
At ₹55/kg, original qty = 770/55 = 14 kg. New price = 0.8*55 = ₹44/kg; new qty = 770/44 = 17.5 kg; increase = 3.5 kg, consistent.

Why Other Options Are Wrong:
₹45, ₹65, ₹37, ₹50 do not satisfy the increase of exactly 3.5 kg when applying a 20% price cut on a ₹770 budget.

Common Pitfalls:
Confusing 20% reduction with 20% more quantity directly. The correct link arises from Money = Price * Quantity and inverse proportionality of price and quantity for fixed money.

Final Answer:
₹ 55 per kg