A Person Had 200/3 Kg Of Rice And Kept 1/10 For Personal Use, Distributing The Rest Among 6 People. How Much Rice Did Each Person Receive?
In this article, we will solve a practical problem involving the distribution of rice. We have a person who possesses a certain quantity of rice, retains a portion for personal use, and then distributes the remainder among a group of people. Our goal is to determine the amount of rice each person receives. This problem involves basic arithmetic operations such as fractions, subtraction, and division, making it an excellent exercise in applying mathematical concepts to real-life scenarios. Understanding how to solve such problems is crucial for developing problem-solving skills and enhancing our ability to handle everyday situations that require mathematical calculations. This article aims to provide a step-by-step solution, ensuring clarity and ease of understanding for readers of all backgrounds. Let's delve into the problem and find out how much rice each person gets.
Problem Statement
A person has 200/3 kg of rice. He keeps 1/10 of it for his own use and distributes the rest among 6 people. How much kg of rice does each person get?
Step-by-Step Solution
To solve this problem, we will follow a step-by-step approach, breaking it down into smaller, manageable parts. This method not only simplifies the calculation process but also enhances understanding and reduces the likelihood of errors. Each step will be clearly explained, ensuring that the logic behind the solution is transparent and easy to follow. By adopting this methodical approach, we can tackle complex problems with greater confidence and accuracy. This step-by-step breakdown will help us to first determine the quantity of rice kept for personal use, then calculate the remaining rice for distribution, and finally, find out how much rice each person receives. Let’s begin by calculating the amount of rice the person keeps for himself.
Step 1: Calculate the Amount of Rice Kept for Personal Use
The person keeps 1/10 of the total rice for personal use. The total amount of rice is 200/3 kg. To find the amount of rice kept, we need to calculate 1/10 of 200/3 kg. This involves multiplying the fraction 1/10 by the quantity 200/3. This calculation is a fundamental arithmetic operation, and understanding how to perform it accurately is essential for solving the problem. By multiplying these values, we will determine the precise amount of rice the person retains for their own use, which is a crucial step in determining the remaining quantity for distribution. This step ensures that we account for the portion of rice that is not distributed, allowing us to calculate the distributed amount accurately.
Amount of rice kept = (1/10) * (200/3) kg
To multiply fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers):
Amount of rice kept = (1 * 200) / (10 * 3) kg
Amount of rice kept = 200 / 30 kg
Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 10:
Amount of rice kept = (200 ÷ 10) / (30 ÷ 10) kg
Amount of rice kept = 20 / 3 kg
So, the person keeps 20/3 kg of rice for personal use.
Step 2: Calculate the Remaining Rice for Distribution
Now that we know the amount of rice kept for personal use, we can calculate the remaining amount that will be distributed among the 6 people. To do this, we subtract the amount kept (20/3 kg) from the total amount of rice (200/3 kg). This subtraction will give us the quantity of rice available for distribution. This step is crucial because it determines the exact amount that will be divided among the individuals, ensuring that we are working with the correct figure. Accurate subtraction is essential here to avoid any errors in the final distribution calculation. Let's perform this subtraction to find out how much rice is left for distribution.
Remaining rice = Total rice - Rice kept
Remaining rice = (200/3) kg - (20/3) kg
Since the denominators are the same, we can subtract the numerators directly:
Remaining rice = (200 - 20) / 3 kg
Remaining rice = 180 / 3 kg
Now, we simplify the fraction by dividing the numerator by the denominator:
Remaining rice = 60 kg
So, there are 60 kg of rice remaining for distribution.
Step 3: Calculate the Amount of Rice Each Person Receives
Finally, we need to determine how much rice each person receives. We have 60 kg of rice to distribute among 6 people. To find the amount each person gets, we divide the total remaining rice (60 kg) by the number of people (6). This division will give us the individual share of rice for each person. This is the final step in solving the problem, and it directly answers the question posed. Accurate division is critical here to ensure that each person receives the correct amount of rice. Let's perform this division to find the answer.
Rice per person = Remaining rice / Number of people
Rice per person = 60 kg / 6 people
Rice per person = 10 kg
Therefore, each person gets 10 kg of rice.
Conclusion
In conclusion, by following a step-by-step approach, we have successfully determined that each person receives 10 kg of rice. We began by calculating the amount of rice the person kept for personal use, which was 20/3 kg. Then, we subtracted this amount from the total rice to find the remaining quantity for distribution, which was 60 kg. Finally, we divided the remaining rice by the number of people to find the individual share, resulting in 10 kg per person. This problem demonstrates the practical application of basic arithmetic operations in everyday scenarios. Understanding how to solve such problems is crucial for developing problem-solving skills and enhancing our ability to handle real-world situations that require mathematical calculations. The methodical approach used here can be applied to various similar problems, making it a valuable tool for learning and practical application. This exercise highlights the importance of accurate calculations and logical thinking in solving quantitative problems.