By selling 90 pens for Rs. 80 a man incurs a loss of 20 percent on the transaction. At what selling price in rupees should he sell the same 90 pens in order to make a profit of 20 percent instead?

Introduction / Context:
This question is a classic example of converting a loss making sale into a profitable one using percentage profit and loss concepts. The seller knows the total selling price at which he suffers a loss and the percentage loss. From that, we can find the total cost price. Once the cost price is known, we can compute the new selling price that would yield a desired profit percentage on the same quantity.

Given Data / Assumptions:

• He sells 90 pens for Rs. 80 and incurs a loss of 20 percent.
• The loss percentage is computed on cost price as usual.
• The quantity in the second case remains 90 pens.
• He wants a profit of 20 percent on the same total cost price.
• We must find the new total selling price for 90 pens.

Concept / Approach:
We first use the loss formula. When there is a 20 percent loss, the selling price equals 80 percent of the cost price. Hence, total cost price equals selling price divided by 0.80. Once we know the total cost price for 90 pens, we use the profit formula. For a 20 percent profit, selling price equals cost price multiplied by 1.20. Since the number of pens is unchanged, there is no need to work on a per pen basis; all calculations can be done on the total amounts.

Step-by-Step Solution:
Total selling price for 90 pens in the first case is 80 rupees.Loss is 20 percent, so selling price equals 80 percent of cost price.Let total cost price be C. Then 0.80 * C equals 80.Therefore, C equals 80 / 0.80 which is 100 rupees.For a 20 percent profit, the new selling price S must be 1.20 times the cost price.So S equals 1.20 * 100 which is 120 rupees.Hence, the 90 pens must be sold for 120 rupees in total to earn a 20 percent profit.

Verification / Alternative check:
We can check our answer by computing percentage profit. At the new selling price of 120 rupees, profit equals 120 minus 100 equals 20 rupees. The percentage profit is 20 divided by 100 multiplied by 100, which is exactly 20 percent. This matches the requirement in the question, so the computed selling price is correct. The arithmetic is simple and consistent with standard percentage formulas.

Why Other Options Are Wrong:
If he sells for 90 rupees, his profit would be 90 minus 100 which is negative 10, a loss of 10 percent. For 100 rupees, there would be neither profit nor loss. For 110 rupees, the profit of 10 rupees on a cost of 100 is only 10 percent. None of these options meet the target profit of 20 percent. Only 120 rupees gives the correct profit percentage.

Common Pitfalls:
Some learners mistakenly use the 20 percent on the selling price to recover cost price, which is incorrect because profit and loss percentages are always based on cost price. Others may try to adjust the selling price directly by adding 40 percent to 80 rupees, forgetting that the base amount for the profit calculation is the cost price, not the earlier selling price. Always identify clearly which value the percentage refers to before performing calculations.

Final Answer:
The man should sell the 90 pens for a total of Rs. 120 to earn a 20 percent profit.