Rs 2186 is divided into M, N and P such that if Rs 26, Rs 28 and Rs 32 are subracted from the share of M, N and P then ratio of their share becomes 9: 13 : 8. Find the share of M.

Options

A. Rs 575
B. Rs 640
C. Rs 656
D. Rs 672

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Define the shares in terms of k
Let the shares of M, N, and P be represented as follows:
- M's share = 9k + 26
- N's share = 13k + 28
- P's share = 8k + 32

### Step 2: Set up the equation for total shares
According to the problem, the total amount shared among M, N, and P is Rs 2186. Therefore, we can write the equation:
\[ (9k + 26) + (13k + 28) + (8k + 32) = 2186 \]

### Step 3: Combine like terms
Now, we will combine the terms on the left side of the equation:
\[ 9k + 13k + 8k + 26 + 28 + 32 = 2186 \]
This simplifies to:
\[ 30k + 86 = 2186 \]

### Step 4: Solve for k
Next, we will isolate k by subtracting 86 from both sides:
\[ 30k = 2186 - 86 \]
Calculating the right side gives:
\[ 30k = 2100 \]
Now, divide both sides by 30:
\[ k = \frac{2100}{30} = 70 \]

### Step 5: Find M's share
Now that we have the value of k, we can find M's share:
\[ M's \, share = 9k + 26 \]
Substituting the value of k:
\[ M's \, share = 9 \times 70 + 26 = 630 + 26 = 656 \]

### Final Answer
Thus, M's share is Rs 656.

---