Solving the Money Distribution Problem

The problem asks us to find the amount Vineet receives from a total of Rs. 2,95,000 distributed among Vineet, Prateek, and Mayank based on specific conditions.

Let's denote the amounts received by each person:

• Vineet's amount = $V$
• Prateek's amount = $P$
• Mayank's amount = $M$

We are given the total amount distributed is Rs. 2,95,000. So, the sum of their amounts is:

$$V + P + M = 295000$$

We are also given two conditions relating their amounts:

1. Vineet gets half of the amount that Mayank gets.
2. Prateek gets Rs. 25,000 less than Vineet.

Let's translate these conditions into equations:

From condition 1:

$$V = \frac{1}{2} M$$

From condition 2:

$$P = V - 25000$$

Finding Vineet's Amount

Our goal is to find the value of $V$. We can use the equations we have to express $P$ and $M$ in terms of $V$ and substitute them into the total amount equation.

From the equation $V = \frac{1}{2} M$, we can solve for $M$ in terms of $V$ by multiplying both sides by 2:

$$M = 2V$$

We already have the equation for $P$ in terms of $V$:

$$P = V - 25000$$

Now, substitute these expressions for $P$ and $M$ into the total amount equation $V + P + M = 295000$:

$$V + (V - 25000) + (2V) = 295000$$

Now, let's solve this equation for $V$:

Combine the terms involving $V$:

$$V + V + 2V - 25000 = 295000$$

$$4V - 25000 = 295000$$

Add 25000 to both sides of the equation:

$$4V = 295000 + 25000$$

$$4V = 320000$$

Divide both sides by 4 to find the value of $V$:

$$V = \frac{320000}{4}$$

$$V = 80000$$

So, the amount Vineet gets is Rs. 80,000.

Verification of Amounts

Let's check if the amounts for Prateek and Mayank add up correctly with Vineet's amount to the total Rs. 2,95,000.

• Vineet's amount $V = 80000$
• Prateek's amount $P = V - 25000 = 80000 - 25000 = 55000$
• Mayank's amount $M = 2V = 2 \times 80000 = 160000$

Total amount = $V + P + M = 80000 + 55000 + 160000 = 295000$.

This matches the given total amount, confirming our calculation for Vineet's share is correct.

Summary of Distribution

Revision Table: Key Steps in Money Distribution Problem

Additional Information: Solving Distribution Problems

Distribution problems often involve dividing a total quantity among individuals based on specific rules or relationships between their shares. These problems can often be solved by setting up equations based on the given conditions.

Common types of relationships include:

• Direct relationships: One person gets a fixed amount more or less than another.
• Proportional relationships: Shares are in a certain ratio (e.g., 2:3:5) or one person gets a fraction or multiple of another's share.
• Percentage relationships: Shares are expressed as percentages of the total or of other shares.

The key is to represent the unknown shares using variables and write down all the given information as algebraic equations. Then, use substitution or elimination methods to solve the system of equations. In many cases, like this problem, expressing all unknowns in terms of a single variable simplifies the process considerably, leading to a single linear equation that can be easily solved.