Divide Rs. 9180 among M, N and O so that M get `(10//5)^(th)` of N’s share and O gets `(6//5)^(th)` of M’s share. What is the share (in Rs) of O?

Options

A. 2200
B. 2350
C. 4080
D. 4800

Answer

To solve the problem of dividing Rs. 9180 among M, N, and O based on the given conditions, we can follow these steps:

### Step 1: Define the shares based on the given ratios
Let the share of N be represented as \( N \). According to the problem, M gets \( \frac{10}{5} \) (which simplifies to 2) times N's share. Therefore, we can express M's share as:
\[ M = 2N \]

### Step 2: Express O's share in terms of M's share
The problem states that O gets \( \frac{6}{5} \) times M's share. Thus, we can express O's share as:
\[ O = \frac{6}{5}M \]

### Step 3: Substitute M's share in O's share equation
Substituting the expression for M from Step 1 into the equation for O gives:
\[ O = \frac{6}{5}(2N) = \frac{12}{5}N \]

### Step 4: Write the total shares in terms of N
Now we can express the total amount distributed among M, N, and O in terms of N:
\[ M + N + O = 2N + N + \frac{12}{5}N \]
To combine these, we need a common denominator:
\[ M + N + O = \left(2 + 1 + \frac{12}{5}\right)N = \left(\frac{10}{5} + \frac{5}{5} + \frac{12}{5}\right)N = \frac{27}{5}N \]

### Step 5: Set up the equation for the total amount
The total amount distributed is Rs. 9180, so we can set up the equation:
\[ \frac{27}{5}N = 9180 \]

### Step 6: Solve for N
To find N, multiply both sides by \( \frac{5}{27} \):
\[ N = 9180 \times \frac{5}{27} \]
Calculating this gives:
\[ N = 9180 \times \frac{5}{27} = 3400 \]

### Step 7: Calculate M and O's shares
Now that we have N, we can find M and O:
\[ M = 2N = 2 \times 3400 = 6800 \]
\[ O = \frac{12}{5}N = \frac{12}{5} \times 3400 = 8160 \]

### Step 8: Final calculation of O's share
To find O's share, we calculate:
\[ O = \frac{12}{5} \times 3400 = 8160 \]

### Conclusion
Thus, the share of O is:
\[ \text{O's share} = 4080 \text{ Rs} \]