sum of Rs 2489 is divided among A, B and C such that if Rs 12, Rs 12 and Rs 5 be diminish from the shares of A, B and C respectively, then their shares will be in the ratio of 5 : 3 : 4. What is the new share (in Rs) of C?

Options

A. 750
B. 1060
C. 1475
D. 820

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We need to divide a total sum of Rs 2489 among A, B, and C. After deducting Rs 12 from A's share, Rs 12 from B's share, and Rs 5 from C's share, their shares will be in the ratio of 5:3:4.

### Step 2: Set Up the Equation
Let the shares of A, B, and C be represented as \( a \), \( b \), and \( c \) respectively. According to the problem, after the deductions, we have:
- A's new share: \( a - 12 \)
- B's new share: \( b - 12 \)
- C's new share: \( c - 5 \)

These new shares are in the ratio of 5:3:4. Therefore, we can express this as:
\[ \frac{a - 12}{5} = \frac{b - 12}{3} = \frac{c - 5}{4} = k \quad \text{(where \( k \) is a constant)} \]

### Step 3: Express Shares in Terms of k
From the ratios, we can express \( a \), \( b \), and \( c \) in terms of \( k \):
\[ a - 12 = 5k \implies a = 5k + 12 \]
\[ b - 12 = 3k \implies b = 3k + 12 \]
\[ c - 5 = 4k \implies c = 4k + 5 \]

### Step 4: Set Up the Total Sum Equation
Now, we know that the total sum of their shares is Rs 2489. Therefore:
\[ a + b + c = 2489 \]
Substituting the expressions for \( a \), \( b \), and \( c \):
\[ (5k + 12) + (3k + 12) + (4k + 5) = 2489 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ 5k + 3k + 4k + 12 + 12 + 5 = 2489 \]
\[ 12k + 29 = 2489 \]

### Step 6: Solve for k
Now, isolate \( k \):
\[ 12k = 2489 - 29 \]
\[ 12k = 2460 \]
\[ k = \frac{2460}{12} = 205 \]

### Step 7: Find the New Share of C
Now that we have \( k \), we can find the new share of C:
\[ c = 4k + 5 = 4(205) + 5 = 820 + 5 = 825 \]

### Step 8: Conclusion
Thus, the new share of C is Rs 825.