Share 30000 bags of 20 kg rice in the ratio [tex]$2: 3: 4: 6$[/tex] among Villages [tex]$A, B, C$[/tex] and [tex]$D$[/tex] in that order. How many bags of 20 kg rice will Villages [tex]$B$[/tex] and [tex]$C$[/tex] get?
Answer (2)
Villages B and C will receive a total of 14000 bags of rice when 30000 bags are shared in the ratio of 2:3:4:6. Village B receives 6000 bags and Village C receives 8000 bags. The total is calculated by first finding the value of x from the ratio and then determining the individual shares for each village.
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The problem involves sharing 30000 bags in the ratio 2 : 3 : 4 : 6 among four villages.
We express the shares as 2 x , 3 x , 4 x , and 6 x , and set up the equation 2 x + 3 x + 4 x + 6 x = 30000 .
Solving for x , we find x = 2000 .
The total number of bags for Villages B and C is 3 x + 4 x = 7 x = 7 ( 2000 ) = 14000 , so the final answer is 14000 .
Explanation
Problem Analysis We are given that 30000 bags of rice are to be shared among four villages, A, B, C, and D, in the ratio 2:3:4:6. Our goal is to determine the total number of bags that villages B and C will receive.
Setting up the Equation Let the number of bags received by villages A, B, C, and D be 2 x , 3 x , 4 x , and 6 x , respectively. The total number of bags is the sum of the bags received by each village, which is given as 30000. Therefore, we can write the equation: 2 x + 3 x + 4 x + 6 x = 30000
Simplifying the Equation Combining the terms on the left side of the equation, we get: 15 x = 30000
Solving for x To solve for x , we divide both sides of the equation by 15: x = 15 30000 = 2000
Calculating Bags for Village B Now that we have the value of x , we can find the number of bags received by villages B and C. Village B receives 3 x bags, so: 3 x = 3 ( 2000 ) = 6000
Calculating Bags for Village C Village C receives 4 x bags, so: 4 x = 4 ( 2000 ) = 8000
Total Bags for Villages B and C Finally, we find the total number of bags received by villages B and C by adding the number of bags each village receives: 6000 + 8000 = 14000 Therefore, villages B and C will get 14000 bags of rice.
Examples
Ratios are commonly used in everyday life for various purposes. For instance, when baking a cake, you might need to mix flour and sugar in a specific ratio, like 2:1. If you're making a larger cake and need to scale up the recipe, understanding ratios helps you maintain the correct proportions of ingredients, ensuring the cake turns out delicious. Similarly, in business, ratios are used to analyze financial statements, compare performance metrics, and make informed decisions about investments and resource allocation. Understanding ratios is therefore a fundamental skill that applies to many real-world scenarios.
