Rice price reduced by 6.25% (i.e., 1/16): With ₹120, Vandana can buy 1 kg more than before. What is the reduced (new) price per kilogram?

Introduction / Context:
Here, a small percent reduction in unit price leads to a unit increase in quantity for a fixed budget. Recognizing 6.25% as 1/16 simplifies the algebra significantly.

Given Data / Assumptions:

• Old price = p (₹/kg); new price = p * (1 − 0.0625) = (15/16) * p.
• Budget = ₹120 (same before and after).
• Quantity increase due to the reduction = 1 kg.

Concept / Approach:
Original quantity = 120/p. New quantity = 120 / ((15/16)p) = 120 * 16 / (15p). The difference equals 1 kg. Solve the resulting linear equation for p and then compute the reduced price (15/16)p.

Step-by-Step Solution:
Increase = 120 * (1/((15/16)p) − 1/p) = 1= 120 * (16/(15p) − 1/p) = 120 * ((16/15 − 1)/p)= 120 * ((1/15)/p) = (120/15) * (1/p) = 8/p8/p = 1 ⇒ p = ₹8 (old price)New price = (15/16)*8 = ₹7.50 per kg

Verification / Alternative check:
Old qty = 120/8 = 15 kg. New price ₹7.50 ⇒ new qty = 120/7.50 = 16 kg. Gain = 1 kg, matches statement.

Why Other Options Are Wrong:
₹9, ₹5.50, ₹19, ₹8 do not yield exactly a 1 kg increase on a ₹120 budget with a 6.25% drop.

Common Pitfalls:
Using 6.25 as 0.625 (tenfold error) or mixing old vs new prices when computing the quantity difference.

Final Answer:
₹ 7.50 per kg