If the price of a pen decreases by 20%, a man can buy 10 more pens for Rs. 100. What is the new price of each pen in rupees?

Introduction / Context:
This question combines percentage decrease in price with a change in quantity purchased for a fixed total amount of money. We are told that after a 20 percent decrease in price, the same amount of money buys 10 more pens. Using this information, we must find the new price per pen. It is a standard type of question in percentage and unitary method topics.

Given Data / Assumptions:
- Let the original price of one pen be P rupees.
- New price after 20% decrease is 0.80P rupees per pen.
- Total money spent in both cases is Rs. 100.
- After the price reduction, the man can buy 10 more pens than before with the same Rs. 100.
- We must find the new price per pen in rupees.

Concept / Approach:
The number of pens purchasable with a fixed amount is equal to total money divided by price per pen. Let the original number of pens be n. Then after the price decrease, the number becomes n + 10. By setting up equations for these quantities using Rs. 100, we can solve for P and then compute the new price 0.80P. The key is to handle the ratio 100 / price carefully and express the change in quantity correctly.

Step-by-Step Solution:
Let original price per pen be P. Original number of pens that can be bought with Rs. 100 = 100 / P. New price per pen after 20% decrease = 0.80P. New number of pens that can be bought with Rs. 100 = 100 / (0.80P). We are told that the man can buy 10 more pens after the price decrease. So, 100 / (0.80P) = 100 / P + 10. Note that 100 / (0.80P) = 100 / (4P / 5) = 100 * (5 / 4P) = 125 / P. Thus the equation becomes 125 / P = 100 / P + 10. Subtract 100 / P from both sides: (125 / P) - (100 / P) = 10. This simplifies to 25 / P = 10. Therefore, P = 25 / 10 = 2.5. So the original price per pen was Rs. 2.50. New price per pen after 20% decrease = 0.80 * 2.5 = 2.0. Hence, the new price per pen is Rs. 2.

Verification / Alternative check:
At original price P = 2.50, the man can buy 100 / 2.50 = 40 pens. At the new price Rs. 2, he can buy 100 / 2 = 50 pens. The difference is 50 - 40 = 10 pens, which matches the condition in the problem. This confirms that the new price of each pen is Rs. 2.

Why Other Options Are Wrong:
1: At this price, 100 / 1 = 100 pens, which is far more than 10 extra pens compared with the original quantity.
4 and 5: These values are larger than the original price 2.5 and would decrease the number of pens the man can buy, not increase it.
3: This price is still higher than 2.5 and would result in fewer pens purchased, not more.

Common Pitfalls:
Some students mistakenly assume that the new price is 20 percent directly of the old price instead of 20 percent less. Others mix up the change in the number of pens and treat 10 as the original number of pens. The correct approach is to express the numbers of pens before and after the price change in terms of P and then use the given difference to form an equation. Careful algebra leads to the correct answer.

Final Answer:
The new price of each pen after the 20 percent decrease is Rs. 2 per pen.