Due to a reduction of 25% in the price of oranges, a customer can now purchase 4 more oranges for Rs. 16 than before. What was the original price of one orange?

Introduction / Context:
This question uses the idea that when a price falls by a certain percentage, the same amount of money can buy more units of the item. It connects percentage change in price with change in quantity purchased and requires setting up an equation involving the original price per unit. It is a common style in quantitative aptitude sections on discounts and unitary method.

Given Data / Assumptions:

• Original price per orange = p rupees (unknown).
• Price is reduced by 25%, so new price per orange = 75% of p.
• A customer spends Rs. 16 both before and after the reduction.
• After the reduction, the customer can buy 4 more oranges for Rs. 16.
• We must find the original value of p.

Concept / Approach:
Let the number of oranges bought before the reduction be n. Then n = 16 / p. After a 25% reduction, the new price is 0.75p, so the new number of oranges is 16 / (0.75p). The difference in quantities is given as 4. We set up an equation representing this difference and solve for p. Working symbolically first keeps the algebra structured and less error-prone.

Step-by-Step Solution:
Step 1: Original price per orange = p. New price after 25% reduction = 0.75p.Step 2: Number of oranges before reduction = 16 / p.Step 3: Number of oranges after reduction = 16 / (0.75p) = 16 / (3p / 4) = (16 * 4) / (3p) = 64 / (3p).Step 4: The customer gets 4 more oranges after the price reduction, so 64 / (3p) - 16 / p = 4.Step 5: Compute the left side: 64 / (3p) - 16 / p = (64 - 48) / (3p) = 16 / (3p).Step 6: So 16 / (3p) = 4, which gives 16 = 12p, so p = 16 / 12 = 4 / 3 ≈ Rs. 1.33.

Verification / Alternative check:
If p = 4 / 3, original price per orange ≈ Rs. 1.33, so original quantity = 16 / (4 / 3) = 16 * 3 / 4 = 12 oranges.New price = 75% of 4 / 3 = 3 / 4 * 4 / 3 = 1 rupee per orange, so new quantity = 16 / 1 = 16 oranges.Difference in quantities = 16 - 12 = 4 oranges, which matches the question.

Why Other Options Are Wrong:
A price of Rs. 1 would lead to 16 oranges both before and after, giving no difference. Prices such as Rs. 1.50 or Rs. 1.60 do not produce a difference of exactly 4 when you redo the calculations. Rs. 0.80 is also inconsistent with both the percentage reduction and the fixed expenditure of Rs. 16. Only Rs. 1.33 (4 / 3) per orange fits all the conditions.

Common Pitfalls:
Many learners forget to express both original and new quantities explicitly, or they mis-handle the 25% reduction by subtracting 0.25 rupees instead of 25% of p. Another common mistake is to take the difference as 4 rupees instead of 4 oranges. Paying attention to units and carefully distinguishing between price and quantity prevents these errors.

Final Answer:
The original price of one orange was approximately Rs. 1.33 (that is, Rs. 4 / 3).