A certain sum is divided between A, B, C and D such that the ratio of shares of A and B is 4:3, that of B and C is 5:8 and that of c and Dis 2: 5. If the difference between the shares of B and Dis 2,250, then the original sum is:
(a)Rs 5800
(b)Rs 5900
(c)Rs 5950
(d)Rs 5850

Options

A. Rs 5,800
B. Rs 5,900
C. Rs 5,950
D. Rs 5,850

Answer

To solve the problem step-by-step, we need to find the original sum divided among A, B, C, and D based on the given ratios and the difference between B's and D's shares.

### Step 1: Establish Ratios
We are given the following ratios:
- A:B = 4:3
- B:C = 5:8
- C:D = 2:5

### Step 2: Express All Shares in Terms of a Common Variable
Let's express the shares of A, B, C, and D in terms of a common variable \( x \).

1. From A:B = 4:3, we can write:
- A = 4x
- B = 3x

2. From B:C = 5:8, we can express C in terms of B:
- Since B = 3x corresponds to 5 parts, we can find the value of C:
- If 5 parts = 3x, then 1 part = \( \frac{3x}{5} \)
- Therefore, C = 8 parts = \( 8 \times \frac{3x}{5} = \frac{24x}{5} \)

3. From C:D = 2:5, we can express D in terms of C:
- Since C = \( \frac{24x}{5} \) corresponds to 2 parts, we can find the value of D:
- If 2 parts = \( \frac{24x}{5} \), then 1 part = \( \frac{12x}{5} \)
- Therefore, D = 5 parts = \( 5 \times \frac{12x}{5} = 12x \)

### Step 3: Write All Shares
Now we have:
- A = 4x
- B = 3x
- C = \( \frac{24x}{5} \)
- D = 12x

### Step 4: Find the Difference Between B and D
We know that the difference between the shares of B and D is given as 2,250:
\[ D - B = 2,250 \]
Substituting the values:
\[ 12x - 3x = 2,250 \]
\[ 9x = 2,250 \]
\[ x = \frac{2,250}{9} = 250 \]

### Step 5: Calculate Individual Shares
Now we can find the individual shares:
- A = \( 4x = 4 \times 250 = 1,000 \)
- B = \( 3x = 3 \times 250 = 750 \)
- C = \( \frac{24x}{5} = \frac{24 \times 250}{5} = 1,200 \)
- D = \( 12x = 12 \times 250 = 3,000 \)

### Step 6: Calculate the Total Sum
Now, we can find the total sum:
\[ \text{Total Sum} = A + B + C + D \]
\[ = 1,000 + 750 + 1,200 + 3,000 \]
\[ = 5,950 \]

### Final Answer
The original sum is Rs 5,950.