Due to an increase of 33.33 percent in the price of apples, a customer can now buy 4 fewer apples for Rs. 16 than before. What was the original price of one apple in paise before the price increase?

Introduction / Context:
This question combines unit price, percentage increase, and change in quantity within a fixed budget. The customer spends the same total amount before and after a price change but can buy fewer apples after the price increases. You need to translate the verbal description into algebra and solve for the original price.

Given Data / Assumptions:

• Original price of one apple = p rupees (unknown).
• Price increases by 33.33 percent, which is effectively one third.
• New price per apple = p * (4 / 3).
• Customer spends Rs. 16 both before and after the price increase.
• After the increase, the customer can buy 4 apples fewer.

Concept / Approach:
The number of apples that can be bought is total money divided by price per unit. Using the original and increased prices, we can express the old and new quantities purchased and then use the fact that the difference between them is 4. This leads to an equation in p that we can solve. Finally we convert the answer into paise by multiplying rupees by 100.

Step-by-Step Solution:
Step 1: Let original price = p rupees per apple. Step 2: After 33.33 percent (one third) increase, new price = (4 / 3) * p. Step 3: Number of apples originally bought = 16 / p. Step 4: Number of apples after the increase = 16 / ((4 / 3) * p) = 16 * (3 / 4p) = 12 / p. Step 5: The customer now buys 4 fewer apples, so (16 / p) − (12 / p) = 4. Step 6: Simplify: (4 / p) = 4, hence p = 1 rupee. Step 7: Convert the original price into paise: 1 rupee = 100 paise.

Verification / Alternative check:
Original price = Rs. 1; with Rs. 16 the customer could buy 16 apples. New price after one third increase = Rs. 4 / 3 per apple. Now the number of apples affordable is 16 * (3 / 4) = 12 apples. The difference is 16 − 12 = 4 apples fewer, exactly as stated in the question, confirming that the computation is correct.

Why Other Options Are Wrong:

• 125, 150, and 400/3 paise correspond to very different original prices and do not produce a difference of 4 apples when the price increases by 33.33 percent.

Common Pitfalls:
A common mistake is to treat 33.33 percent as exactly 1/3 without adjusting carefully or to set up the quantity difference equation incorrectly. Another error is forgetting to convert rupees to paise at the end. Always keep track of units and carefully form the relationship between old and new quantities.

Final Answer:
The original price of one apple was 100 paise (that is, Rs. 1).