A quantity of tea is sold at Rs. 5.75 per kilogram and the total profit on the sale is Rs. 60. If the trader makes a profit of exactly 15 percent on the deal, what is the total quantity of tea (in kilograms) that is sold?

Introduction / Context:
This aptitude question checks the basic concepts of profit and loss, especially how to relate the selling price per kilogram, cost price per kilogram, total profit, and total quantity sold. Such questions are common in banking exams, SSC exams, and other competitive tests that include quantitative aptitude sections.

Given Data / Assumptions:

• Selling price per kilogram of tea (SP) = Rs. 5.75
• Profit percentage on cost price = 15 percent
• Total profit earned on the transaction = Rs. 60
• We assume all tea is sold at the same rate without any wastage.

Concept / Approach:
The key idea is that profit is the difference between selling price and cost price multiplied by the quantity. When we know the profit percentage and selling price per kilogram, we can compute the cost price per kilogram. Once the per kilogram profit is known, dividing the total profit by profit per kilogram gives the total quantity of tea sold.

Step-by-Step Solution:
Let cost price per kilogram be CP. Given profit percent = 15 percent, so SP = CP * (1 + 15 / 100). Therefore SP = CP * 1.15. We know SP = 5.75, so 5.75 = 1.15 * CP. Thus CP = 5.75 / 1.15 = 5 rupees per kilogram. Profit per kilogram = SP - CP = 5.75 - 5.00 = 0.75 rupees per kilogram. Total profit = profit per kilogram * quantity. 60 = 0.75 * quantity. Quantity = 60 / 0.75 = 80 kilograms.

Verification / Alternative check:
If quantity is 80 kg, total cost = 80 * 5 = Rs. 400. Total selling price = 80 * 5.75 = Rs. 460. Profit = 460 - 400 = Rs. 60, which matches the given profit. The computed quantity is therefore consistent with the given information.

Why Other Options Are Wrong:
72 kg: Profit would be 72 * 0.75 = Rs. 54, which is less than Rs. 60. 76 kg: Profit would be 76 * 0.75 = Rs. 57, still not Rs. 60. 84 kg: Profit would be 84 * 0.75 = Rs. 63, which is greater than Rs. 60. Thus only 80 kg gives the correct profit of Rs. 60.

Common Pitfalls:
Students sometimes treat profit percent as a percentage of selling price instead of cost price, which is wrong here. Another frequent mistake is to try to work directly with percentages without first finding the cost price, which makes the calculations confusing. Forgetting that profit per kilogram is needed before using the total profit formula can also lead to errors.

Final Answer:
The total quantity of tea sold is 80 kg.