A sum of Rs 340.68 is distributed among L, M and N such that L gets Rs 5.72 more than N and M gets Rs. 2.24 more than L. N gets

Options

A. Rs 109
B. Rs 110.90
C. Rs 113.56
D. Rs 114.72

Answer

To solve the problem step by step, we will first define the amounts received by L, M, and N based on the information provided.

### Step 1: Define the variables
Let:
- N = amount received by N
- L = amount received by L
- M = amount received by M

From the problem, we know:
- L gets Rs 5.72 more than N:
\( L = N + 5.72 \)
- M gets Rs 2.24 more than L:
\( M = L + 2.24 \)

### Step 2: Substitute L in terms of N into M's equation
Substituting the expression for L into M's equation:
\( M = (N + 5.72) + 2.24 \)
This simplifies to:
\( M = N + 5.72 + 2.24 \)
\( M = N + 7.96 \)

### Step 3: Write the equation for the total amount
According to the problem, the total amount distributed among L, M, and N is Rs 340.68:
\( L + M + N = 340.68 \)

Substituting the expressions for L and M in terms of N:
\( (N + 5.72) + (N + 7.96) + N = 340.68 \)

### Step 4: Combine like terms
Combining the terms gives:
\( N + 5.72 + N + 7.96 + N = 340.68 \)
This simplifies to:
\( 3N + 13.68 = 340.68 \)

### Step 5: Solve for N
Now, we will isolate N:
Subtract 13.68 from both sides:
\( 3N = 340.68 - 13.68 \)
\( 3N = 327 \)

Now, divide by 3:
\( N = \frac{327}{3} \)
\( N = 109 \)

### Step 6: Conclusion
N receives Rs 109.