The sum of Rs. 2495 is divided among A, B and C such that if we decrease Rs. 15 of share A, Rs. 30 of share B and Rs. 50 of share C. Then the ratio become 3 :2:7. What are the share of A, B and C.

Options

A. `615, 430, 1450`
B. `620, 435, 1425`
C. `600, 400, 140`
D. `620, 420, 1400`

Answer

To solve the problem of dividing Rs. 2495 among A, B, and C, given the conditions of the problem, we will follow these steps:

### Step 1: Define the Shares
Let the shares of A, B, and C be represented as:
- A = share of A
- B = share of B
- C = share of C

According to the problem, we have:
\[ A + B + C = 2495 \]

### Step 2: Set Up the Ratios
The problem states that if we decrease Rs. 15 from A's share, Rs. 30 from B's share, and Rs. 50 from C's share, the new ratio becomes 3:2:7. We can express this mathematically as:
- A - 15 = 3k
- B - 30 = 2k
- C - 50 = 7k

where k is a common factor.

### Step 3: Express A, B, and C in Terms of k
From the equations above, we can express A, B, and C in terms of k:
1. \( A = 3k + 15 \)
2. \( B = 2k + 30 \)
3. \( C = 7k + 50 \)

### Step 4: Substitute into the Total Sum Equation
Now we substitute the expressions for A, B, and C back into the total sum equation:
\[ (3k + 15) + (2k + 30) + (7k + 50) = 2495 \]

### Step 5: Simplify the Equation
Combining like terms, we get:
\[ 3k + 2k + 7k + 15 + 30 + 50 = 2495 \]
\[ 12k + 95 = 2495 \]

### Step 6: Solve for k
Now, we isolate k:
\[ 12k = 2495 - 95 \]
\[ 12k = 2400 \]
\[ k = \frac{2400}{12} = 200 \]

### Step 7: Find A, B, and C
Now that we have the value of k, we can find A, B, and C:
1. For A:
\[ A = 3k + 15 = 3(200) + 15 = 600 + 15 = 615 \]
2. For B:
\[ B = 2k + 30 = 2(200) + 30 = 400 + 30 = 430 \]
3. For C:
\[ C = 7k + 50 = 7(200) + 50 = 1400 + 50 = 1450 \]

### Final Shares
Thus, the shares of A, B, and C are:
- A = Rs. 615
- B = Rs. 430
- C = Rs. 1450