Points to Remember:
- This is a ratio and proportion problem.
- We need to find a common ratio between A, B, and C to determine their individual shares.
- The total amount is â¹4700.
Introduction:
This question involves the concept of ratio and proportion, a fundamental aspect of mathematics used to compare quantities. We are given the ratios between the shares of three individuals, A, B, and C, and the total amount to be divided. Our task is to determine the share received by C. Solving this requires finding a common ratio that allows us to express the shares of A, B, and C in terms of a single unit.
Body:
1. Finding a Common Ratio:
We are given A:B = 5:6 and B:C = 10:13. To find the common ratio, we need to make the ratio of B the same in both. We can multiply the first ratio by 5/5 and the second ratio by 1/1 to achieve this:
- A:B = 5:6 becomes 25:30 (multiplying by 5/5)
- B:C = 10:13 becomes 30:39 (multiplying by 3/3)
Now we have a common ratio for B, allowing us to express the shares as: A:B:C = 25:30:39
2. Calculating Individual Shares:
The total ratio is 25 + 30 + 39 = 94. This means that the total amount (â¹4700) is divided into 94 parts.
- Share of A = (25/94) * â¹4700 = â¹1250
- Share of B = (30/94) * â¹4700 = â¹1500
- Share of C = (39/94) * â¹4700 = â¹1950
3. Verifying the Solution:
The sum of the individual shares should equal the total amount: â¹1250 + â¹1500 + â¹1950 = â¹4700. This confirms our calculations are correct.
Conclusion:
The share of C is â¹1950. This problem demonstrates the application of ratio and proportion in solving real-world distribution problems. By finding a common ratio and expressing the shares proportionally, we can accurately determine the individual amounts. This method can be applied to various scenarios involving the division of resources or assets based on predetermined ratios. The accuracy of the solution highlights the importance of understanding and applying fundamental mathematical concepts for fair and equitable distribution. This approach ensures transparency and avoids any potential disputes arising from unequal distribution.