An amount of money is to be divided between P, Q and R in the ratio of 2: 5:7 respectively. If the total of P's and R's share is Rs. 800 more than Q's share. What will be P's share in it?

Answer

To solve the problem step by step, we will follow the logic outlined in the video transcript.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The amounts are to be divided between P, Q, and R in the ratio of 2:5:7. This means:
- P's share = 2 parts
- Q's share = 5 parts
- R's share = 7 parts

2. **Assign Variables**:
Let's assign a variable to each part of the ratio. We can let:
- P's share = 2x
- Q's share = 5x
- R's share = 7x

3. **Set Up the Equation**:
According to the problem, the total of P's and R's share is Rs. 800 more than Q's share. We can express this mathematically:
\[ P + R = Q + 800 \]
Substituting the expressions for P, Q, and R, we get:
\[ 2x + 7x = 5x + 800 \]

4. **Simplify the Equation**:
Combine like terms:
\[ 9x = 5x + 800 \]
Now, subtract 5x from both sides:
\[ 9x - 5x = 800 \]
This simplifies to:
\[ 4x = 800 \]

5. **Solve for x**:
Divide both sides by 4:
\[ x = \frac{800}{4} = 200 \]

6. **Find P's Share**:
Now that we have the value of x, we can find P's share:
\[ P's \, share = 2x = 2 \times 200 = 400 \]

### Final Answer:
P's share is Rs. 400.