A rice trader buys 25 quintals of rice for a total of Rs. 1825. During transportation, 27 percent of the rice is lost. At what selling price per quintal should he sell the remaining rice in order to earn a profit of 20 percent on his total investment?

Introduction / Context:
This question involves both loss of quantity and profit on cost, a situation that appears frequently in commercial aptitude problems. The trader loses a certain percentage of the physical quantity during transportation, but wants to maintain a target overall profit on the total money invested. We must therefore work with total cost, remaining quantity, and required selling price per unit to reach the desired profit.

Given Data / Assumptions:

• Total quantity bought is 25 quintals.
• Total cost price is Rs. 1825.
• Loss in transportation is 27 percent of the quantity.
• Target profit on total cost is 20 percent.
• We must find the required selling price per quintal for the remaining rice.

Concept / Approach:
The main steps are: first, compute the quantity of rice remaining after the transportation loss. Second, calculate the required total revenue to achieve a 20 percent profit on the initial cost. Finally, divide this required total revenue by the remaining quantity to get the required selling price per quintal. It is very important to realize that the profit percentage is calculated on the original cost, regardless of the quantity lost.

Step-by-Step Solution:
Total cost price equals 1825 rupees.Initial quantity equals 25 quintals.Loss in transportation is 27 percent, so remaining quantity equals 73 percent of 25 quintals.Remaining quantity equals 0.73 * 25 which is 18.25 quintals.To earn a profit of 20 percent on the cost, total revenue required equals 1.20 * 1825.Compute required revenue as 1.20 * 1825 which is 2190 rupees.Required selling price per quintal equals total required revenue divided by remaining quantity, that is 2190 / 18.25.2190 divided by 18.25 equals 120 rupees per quintal.

Verification / Alternative check:
We can verify by checking the actual profit at this selling price. Selling 18.25 quintals at Rs. 120 per quintal yields 18.25 * 120 which is 2190 rupees in total. Profit equals 2190 minus 1825 which is 365 rupees. Percentage profit equals 365 divided by 1825 multiplied by 100, which is exactly 20 percent. Therefore, the selling price of 120 rupees per quintal satisfies the condition for the desired profit even after the transportation loss.

Why Other Options Are Wrong:
At 44.4 rupees per quintal, the total revenue would be far below the cost, leading to a loss rather than a profit. At 87.6 rupees per quintal or 115.8 rupees per quintal, the total revenue would not reach 2190 rupees and thereby would not provide a full 20 percent profit on 1825 rupees. Only 120 rupees per quintal gives the exact required total revenue to achieve the target profit.

Common Pitfalls:
Some learners incorrectly calculate the 20 percent profit on the reduced quantity instead of the original cost, which changes the base incorrectly. Others forget to adjust the quantity after the 27 percent loss and simply divide the required revenue by the original 25 quintals. It is crucial to separate the concepts: profit is on cost, while selling price per quintal depends on how much quantity is left for sale after losses in transportation.

Final Answer:
The trader should sell the remaining rice at Rs. 120 per quintal to earn a 20 percent profit on his investment.