Price of rice increased by 25%: A buyer can purchase 20 kg less for ₹400 after the increase. What is the new price per kilogram?

Introduction / Context:
This question links a percentage increase in price to a decrease in quantity for a fixed budget. By modeling prices before and after the change and using the observed reduction in quantity, we can find the increased price per kilogram.

Given Data / Assumptions:

• Budget = ₹400, unchanged before and after.
• Price increases by 25% (new price = 1.25 * old price).
• Quantity falls by 20 kg due to the increase.

Concept / Approach:
Let old price be p. Then original quantity = 400/p. New price = 1.25p, so new quantity = 400/(1.25p). The observed reduction is 20 kg. Set up the equation and solve for p, then compute the new price 1.25p.

Step-by-Step Solution:
400/p − 400/(1.25p) = 20400/p * (1 − 1/1.25) = 201 − 1/1.25 = 1 − 0.8 = 0.2(400/p) * 0.2 = 20 ⇒ 80/p = 20 ⇒ p = 4New price = 1.25 * 4 = ₹5 per kg

Verification / Alternative check:
Old qty = 400/4 = 100 kg. New qty = 400/5 = 80 kg. Reduction = 20 kg, matching the statement.

Why Other Options Are Wrong:
₹6 and ₹10 mismatch the 20 kg drop; ₹4 is the old price, not the new one; ₹8 is not supported by the fixed-budget math.

Common Pitfalls:
Confusing new price with old price or adding absolute rupees instead of working proportionally with price and quantity.

Final Answer:
₹ 5