Understanding the Money Division Problem

This problem involves dividing a total amount of money, ₹5,110, among three people: Rajesh, Vivek, and Kripal. The division is not equal; it follows specific ratios based on how much each person receives relative to others. We are given the following conditions:

• Rajesh gets double the amount that Vivek gets.
• Kripal gets double the amount that Rajesh gets.

Our goal is to find out how much money Kripal will receive.

Setting Up the Shares Using Ratios

To solve this type of ratio problem, it's helpful to represent the shares in terms of a single variable. Let's start with the person who receives the smallest relative amount, which is Vivek.

• Let Vivek's share be represented by \(x\).
• According to the problem, Rajesh gets double the amount Vivek gets. So, Rajesh's share is \(2 \times \text{Vivek's share} = 2 \times x = 2x\).
• Next, Kripal gets double the amount Rajesh gets. So, Kripal's share is \(2 \times \text{Rajesh's share} = 2 \times (2x) = 4x\).

Now we have the shares of all three people in terms of \(x\):

• Vivek's share: \(x\)
• Rajesh's share: \(2x\)
• Kripal's share: \(4x\)

Calculating the Total Share and Solving for x

The total amount of money shared is ₹5,110. This total amount is the sum of the shares of Rajesh, Vivek, and Kripal.

Total amount = Vivek's share + Rajesh's share + Kripal's share

In terms of \(x\):

\(5110 = x + 2x + 4x\)

Combine the terms on the right side:

\(5110 = (1 + 2 + 4)x\)

\(5110 = 7x\)

Now, to find the value of \(x\), we need to divide the total amount by the sum of the ratio parts (which is 7).

\(x = \frac{5110}{7}\)

Finding the Value of x

Let's perform the division:

\(5110 \div 7\)

\(51 \div 7 = 7\) with a remainder of \(2\) (\(7 \times 7 = 49\))

Bring down the next digit (\(1\)), making the new number \(21\).

\(21 \div 7 = 3\) with a remainder of \(0\) (\(7 \times 3 = 21\))

Bring down the last digit (\(0\)).

\(0 \div 7 = 0\)

So, \(x = 730\).

Determining Kripal's Share

We found that \(x = 730\). Now we can find the share of each person:

• Vivek's share: \(x = ₹730\)
• Rajesh's share: \(2x = 2 \times 730 = ₹1460\)
• Kripal's share: \(4x = 4 \times 730 = ₹2920\)

We can verify if the total is correct:

\(730 + 1460 + 2920 = ₹5110\)

The total matches the given amount, so our calculations are correct.

The question asks for Kripal's share, which we found to be ₹2,920.

Summary of Shares

Therefore, Kripal will get ₹2,920.

Revision Table: Money Division Ratios

Additional Information: Proportional Distribution

This problem is an example of proportional distribution or sharing in a given ratio. When a total quantity is divided among individuals or categories based on ratios, the individual amounts are proportional to their respective ratio parts. The sum of the ratio parts corresponds to the total quantity.

In this case, the shares are in the ratio \(x : 2x : 4x\), which simplifies to the ratio \(1 : 2 : 4\) for Vivek, Rajesh, and Kripal, respectively. This means for every ₹1 Vivek gets, Rajesh gets ₹2, and Kripal gets ₹4. The total ratio parts are \(1 + 2 + 4 = 7\).

So, Vivek gets \(\frac{1}{7}\) of the total, Rajesh gets \(\frac{2}{7}\) of the total, and Kripal gets \(\frac{4}{7}\) of the total amount ₹5,110.

• Vivek's share = \(\frac{1}{7} \times 5110 = 730\)
• Rajesh's share = \(\frac{2}{7} \times 5110 = 2 \times 730 = 1460\)
• Kripal's share = \(\frac{4}{7} \times 5110 = 4 \times 730 = 2920\)

This confirms our earlier result using the variable method. Both methods yield the same answer and illustrate the concept of dividing an amount according to a given ratio or proportion.