How To Distribute Amounts Equally and Then Redistribute in a Fair Manner

When dealing with financial distributions, it is often essential to understand how to distribute amounts equally and then redistribute them fairly. This involves both arithmetic and algebraic reasoning. In this article, we will walk through a practical example that combines these concepts.

Consider an amount of Rs 113,373 distributed equally amongst 57 persons. After distribution, one person gives some money to another such that the giver's amount becomes 1/3 of the recipient's amount. This problem requires a step-by-step approach to determine the amount given.

Step 1: Calculating the Initial Distribution

Let us start with the straightforward step: calculating the amount each person receives from the total amount distributed equally among 57 persons.

Step 1: Calculate the amount per person.

Amount per person (frac{113373}{57} approx 1985.61)

Step 2: Defining the Variables

Let's denote the amount received by the person who gives money as (x) and the amount received by the person who receives money as (y). Based on the problem statement, after the transaction, the amount the first person has is (x - d), and the second person has (y d), where (d) is the amount given by the first person to the second. The problem states that the initial amounts for both (x) and (y) are the same, i.e., 1985.61.

Step 3: Setting Up the Equation

The relation between the amounts after the transaction can be mathematically expressed as:

[x - d frac{1}{3} (y d)]

Step 4: Substituting the Values

Substituting the values of (x) and (y) from the initial distribution:

[1985.61 - d frac{1}{3} (1985.61 d)]

Step 5: Simplifying the Equation

Let's simplify the equation by multiplying both sides by 3 to eliminate the fraction:

[3(1985.61 - d) 1985.61 d]

This simplifies to:

[5956.83 - 3d 1985.61 d]

Step 6: Rearranging the Equation

Rearrange the equation to isolate (d) on one side:

[5956.83 - 1985.61 3d d]

This further simplifies to:

[3971.22 4d]

Step 7: Solving for (d)

Solving for (d) gives:

[d frac{3971.22}{4} approx 992.81]

Conclusion

The amount that one person gave to another is approximately Rs 992.81.

An Example for Additional Clarity

For an additional point of reference, let's solve a similar problem:

Total amount distributed Rs 113,373.

Hence, share of each Rs 1989 (since (frac{113373}{57} approx 1989)).

Now, let (x) be the amount given by one to another. Then, the equation becomes:

Rs 1989 - (x) (frac{1}{3})(Rs 1989 (x))

Solving this, we get:

2(1989) 4(x)

(x) Rs 994.5.

Thus, A gives Rs 994.5 to B.

Conclusion and Summary

In conclusion, understanding how to distribute amounts equally and then fairly redistribute them is crucial in practical scenarios. The steps outlined above provide a clear method to address such problems. Whether it be Rs 113,373 or other amounts, the process remains the same. This approach combines basic arithmetic and algebra to reach a fair and balanced solution.

Problems like these not only enhance one's mathematical skills but also prepare them for real-world financial situations where precision is crucial.