Distributing Money Among Friends in a Specific Ratio

When distributing a sum of money among friends in a given ratio, it is crucial to understand the relationship between the shares each person receives. Let's explore a situation where three friends, A, B, and C, receive money in the ratio 2:4:6. We will solve the problem step by step to determine how much C gets.

Step-by-Step Solution

Given that the ratio is 2:4:6, we can represent the shares of A, B, and C as 2x, 4x, and 6x, respectively, where x is a common multiplication factor.

According to the problem, B gets Rs. 10 more than A. Therefore, we can write:

4x 2x 10

Subtracting 2x from both sides, we get:

2x 10

Dividing both sides by 2, we find:

x 5

With x determined, we can now calculate C's share, which is 6x:

6x 6 * 5 30

Another Approach with Different Ratios

Let's consider an alternative scenario where the ratio is adjusted to 2:4:14. In this case, we can represent the shares as A 2x, B 4x, and C 14x.

We know that B gets 10 more than A:

4x 2x 10

Subtracting 2x from both sides, we get:

2x 10

Dividing both sides by 2, we find:

x 5

Now, we can determine C's share, which is 14x:

14x 14 * 5 70

Common Errors in Ratio Distribution

It is important to note that if the problem statement initially seems incorrect, such as B receiving 16 rupees more than A, the ratio must be reconsidered. In such a case, the correct ratio would be 5:4:20, where:

If B gets 16 more than A, then:

5x - 4x 16

Therefore:

x 16

Given that C's share is 4x (the next term in the ratio 5:4:20), we get:

20 * 16 320

Conclusion

To summarize, understanding the ratio and correctly interpreting the conditions given in the problem is key to solving these types of distribution problems. Using a common multiple x, we can easily calculate the shares of each individual.

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