A sum of Rs. 4,300 is distributed among M, N and O, such that M receives 25% more than N and N receives 25% less than O. What is O’s share in the amount?

Options

A. A) 1564
B. B) 1600
C. C) 1632
D. D) 1714

Answer

To solve the problem of distributing Rs. 4,300 among M, N, and O, we can follow these steps:

### Step 1: Define the shares
Let O's share be Rs. P. According to the problem, N receives 25% less than O. Therefore, we can express N's share as:
\[ N = P - 0.25P = 0.75P = \frac{3P}{4} \]

### Step 2: Determine M's share
M receives 25% more than N. So, we can express M's share as:
\[ M = N + 0.25N = 1.25N = 1.25 \times \frac{3P}{4} = \frac{15P}{16} \]

### Step 3: Write the equation for total shares
Now, we have the shares of M, N, and O:
- M's share = \(\frac{15P}{16}\)
- N's share = \(\frac{3P}{4}\)
- O's share = \(P\)

The total amount distributed among M, N, and O is Rs. 4,300. Therefore, we can write the equation:
\[ M + N + O = 4300 \]
Substituting the values we found:
\[ \frac{15P}{16} + \frac{3P}{4} + P = 4300 \]

### Step 4: Find a common denominator and simplify
The common denominator for the fractions is 16. We can rewrite \(\frac{3P}{4}\) as \(\frac{12P}{16}\):
\[ \frac{15P}{16} + \frac{12P}{16} + \frac{16P}{16} = 4300 \]
Combining the fractions:
\[ \frac{15P + 12P + 16P}{16} = 4300 \]
This simplifies to:
\[ \frac{43P}{16} = 4300 \]

### Step 5: Solve for P
To isolate P, we can multiply both sides by 16:
\[ 43P = 4300 \times 16 \]
Calculating the right side:
\[ 43P = 68800 \]
Now, divide both sides by 43:
\[ P = \frac{68800}{43} = 1600 \]

### Step 6: Determine O's share
Now that we have O's share:
\[ O = P = 1600 \]

### Conclusion
O's share in the amount is Rs. 1,600.

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