The price of oranges is increased by 30%, and after this increase a person can buy 12 fewer oranges for Rs 208 than before. What was the original price in rupees of one orange before the 30% increase?

Introduction / Context:
This question is a classic application of percentage increase and basic algebra in a real-life context involving the price of fruits. You are given how many fewer oranges can be bought after a price hike and asked to work backwards to find the original price per orange before the increase took place.

Given Data / Assumptions:

• Total money spent each time = Rs 208.
• Original price per orange = Rs p (unknown).
• Price increased by 30%, so new price = 1.3 * p.
• After the increase, the buyer can purchase 12 fewer oranges with the same Rs 208.

Concept / Approach:
If a person spends the same amount of money but the price per unit increases, the number of units that can be bought decreases. Let the original number of oranges be N. After the price increase, the number becomes N − 12. Using the relationships money = price * quantity before and after the increase, we can form an equation in terms of p and solve it.

Step-by-Step Solution:
Step 1: Let the original price per orange be p rupees. Step 2: The original number of oranges that can be bought is 208 / p. Step 3: After a 30% increase, the new price is 1.3 * p. Step 4: With the new price, the number of oranges that can be bought is 208 / (1.3 * p). Step 5: According to the question, the new number of oranges is 12 less than the original number: 208 / (1.3 * p) = 208 / p − 12. Step 6: Express 1.3 as 13 / 10 and rewrite: 208 * 10 / (13p) = 208 / p − 12. Step 7: Multiply both sides by p to remove the denominator: 2080 / 13 = 208 − 12p. Step 8: Simplify 2080 / 13 = 160, so 160 = 208 − 12p. Step 9: Rearrange: 12p = 208 − 160 = 48, so p = 48 / 12 = 4. Step 10: Therefore, the original price per orange was Rs 4.

Verification / Alternative check:
At Rs 4 per orange, the buyer could originally buy 208 / 4 = 52 oranges. After a 30% increase, the new price is 4 * 1.3 = Rs 5.20. At Rs 5.20 per orange, the buyer can buy 208 / 5.20 = 40 oranges. The decrease is 52 − 40 = 12 oranges, which matches the condition in the question.

Why Other Options Are Wrong:
Rs 2, Rs 3, Rs 6 and Rs 8 do not satisfy the condition that the difference in quantity is exactly 12 when the price increases by 30%. Substituting these values into the equation gives fewer or more than 12 oranges difference.

Common Pitfalls:
Students sometimes forget to convert 30% into a multiplier of 1.3 or set up the relationship between the two quantities incorrectly. It is also easy to make algebraic errors while clearing denominators. Writing the equations clearly and simplifying step by step helps avoid mistakes.

Final Answer:
The original price of one orange was Rs 4.