A certain sum is divided between A, B, C and D such that the ratio of the shares of A and B is 1:3, that of B and C is 2:5, and that of C and D is 2:3. If the difference between the shares of A and C is Rs 3,510, then the share of D is:

Options

A. Rs 6,075
B. Rs 4,050
C. Rs 4,320
D. Rs 3,240

Answer

To solve the problem step by step, we will first establish the ratios and then find the share of D based on the given information.

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

Let’s express the shares of A, B, C, and D in terms of a common variable.

Let:
- A = 1x
- B = 3x (from A : B = 1 : 3)

From B : C = 2 : 5, we can express C in terms of B:
- B = 2y
- C = 5y

Since B is also equal to 3x, we can equate:
3x = 2y
=> y = (3/2)x

Now substituting y in C:
C = 5y = 5 * (3/2)x = (15/2)x

Now, we need to express D in terms of C:
From C : D = 2 : 3, we have:
- C = 2z
- D = 3z

Since C is also equal to (15/2)x, we can equate:
(15/2)x = 2z
=> z = (15/4)x

Now substituting z in D:
D = 3z = 3 * (15/4)x = (45/4)x

### Step 2: Combine the Ratios
Now we have:
- A = 1x
- B = 3x
- C = (15/2)x
- D = (45/4)x

### Step 3: Find the Difference Between A and C
We know that the difference between the shares of A and C is Rs. 3,510:
A - C = 3,510
=> 1x - (15/2)x = 3,510
=> (2/2)x - (15/2)x = 3,510
=> (-13/2)x = 3,510

### Step 4: Solve for x
Now, we solve for x:
=> x = 3,510 * (-2/13)
=> x = -3,510 * 2 / 13
=> x = -7,020 / 13
=> x = 540

### Step 5: Find the Share of D
Now we can find the share of D:
D = (45/4)x
=> D = (45/4) * 540
=> D = 45 * 135
=> D = 6,075

Thus, the share of D is Rs. 6,075.

### Final Answer
The share of D is Rs. 6,075.

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