Divide Rs 5100 among M, N and O so that M get `(8//11)^(th)` of N's share and O gets `(7//6)^(th)` of M's share. What is the share (in Rs) of N?

Options

A. 1488
B. 1980
C. 1680
D. 2200

Answer

To solve the problem of dividing Rs 5100 among M, N, and O, we will denote their shares as follows:

Let:
- M's share = A
- N's share = B
- O's share = C

According to the problem:
1. M gets \( \frac{8}{11} \) of N's share:
\[ A = \frac{8}{11}B \]

2. O gets \( \frac{7}{6} \) of M's share:
\[ C = \frac{7}{6}A \]

We also know that the total amount shared among M, N, and O is Rs 5100:
\[ A + B + C = 5100 \]

### Step 1: Substitute A and C in terms of B

From the first equation, we can express A in terms of B:
\[ A = \frac{8}{11}B \]

Now substituting A into the equation for C:
\[ C = \frac{7}{6}A = \frac{7}{6} \left( \frac{8}{11}B \right) = \frac{56}{66}B = \frac{28}{33}B \]

### Step 2: Substitute A and C into the total amount equation

Now we can substitute A and C back into the total amount equation:
\[ \frac{8}{11}B + B + \frac{28}{33}B = 5100 \]

### Step 3: Find a common denominator

The common denominator for the fractions \( \frac{8}{11} \), \( 1 \) (which is \( \frac{33}{33} \)), and \( \frac{28}{33} \) is 33. We rewrite the equation:
\[ \frac{24}{33}B + \frac{33}{33}B + \frac{28}{33}B = 5100 \]

### Step 4: Combine the fractions

Combining the fractions gives:
\[ \frac{24B + 33B + 28B}{33} = 5100 \]
\[ \frac{85B}{33} = 5100 \]

### Step 5: Solve for B

To isolate B, multiply both sides by 33:
\[ 85B = 5100 \times 33 \]
\[ 85B = 168300 \]

Now divide both sides by 85:
\[ B = \frac{168300}{85} = 1980 \]

### Conclusion

Thus, N's share (B) is Rs 1980.