Introduction

Sharing a sum of money among several individuals in a specific ratio is a common problem that often arises in financial planning and mathematics. This article will guide you through solving an interesting sharing problem where Rs 3500 is to be divided among three individuals based on a specific relationship between their shares. We will tackle this problem step by step using clear mathematical reasoning and calculations.

Problem Presentation

The problem states that Rs 3500 has to be shared among three individuals in such a way that the first individual gets 50% of what the second individual gets, and the second individual gets 50% of what the third individual gets.

Step-by-Step Solution

We denote the amount received by the third individual as x.

According to the problem:

The second individual gets 50% of the third individual's share, i.e., 0.5x. The first individual gets 50% of the second individual's share, i.e., 0.5 * 0.5x 0.25x.

To find the specific amounts, we need to write and solve an equation for the total amount:

0.25x 0.5x x 3500.

Combining the terms, we get:

1.75x 3500.

Now, solving for x:

x 3500 / 1.75 2000.

Calculating Each Share

Now that we have determined the value of x, we can calculate the portions for each individual:

The third individual gets: x 2000. The second individual gets: 0.5x 0.5 * 2000 1000. The first individual gets: 0.25x 0.25 * 2000 500.

Thus, the amounts received by each individual are:

The first individual: Rs 500. The second individual: Rs 1000. The third individual: Rs 2000.

Alternative Solution Using Simplified Methods

An alternative, easier method to solve this problem involves conceptualizing the distribution based on the lowest share. Let x be the amount received by the third individual. The second individual receives 0.5x, and the first individual receives 0.25x. The sum of these shares is:

x 0.5x 0.25x 3500.

Simplifying this gives:

2.75x 3500.

Solving for x:

x 3500 / 2.75 ≈ 1263.20.

Revising the steps for specific calculations:

The third individual receives x 2000 (as previously calculated). The second individual receives: 0.5 * 2000 1000. The first individual receives: 0.25 * 2000 500.

Conclusion

This sharing problem can be effectively solved using algebraic methods or simple proportional reasoning, leading to the conclusion that each individual receives Rs 500, Rs 1000, and Rs 2000 respectively when sharing Rs 3500 among three people according to the given ratios.