A certain sum is divided between A. B, C and D such that the ratio of the shares of A and B is `3 : 4`, that of B and C is `5: 6` and that of C and D is `9: 10`. If the difference between the shares of A and C is Rs. `3,240`, then what is the share of D?

Options

A. a) Rs. 9,520
B. b) Rs. 8,800
C. c) Rs. 8,640
D. d) Rs. 9,600

Answer

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

### Step 1: Establish Ratios
We know the following ratios:
- A : B = 3 : 4
- B : C = 5 : 6
- C : D = 9 : 10

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

Let:
- A = 3x
- B = 4x (from A : B = 3 : 4)

Now, since B = 4x, we can find C:
- B : C = 5 : 6 ⇒ C = (6/5) * B = (6/5) * 4x = (24/5)x

Now we can find D using C:
- C : D = 9 : 10 ⇒ D = (10/9) * C = (10/9) * (24/5)x = (240/45)x = (16/3)x

### Step 3: Find the Difference Between A and C
According to the problem, the difference between the shares of A and C is Rs. 3,240:
- A - C = 3x - (24/5)x = (15/5)x - (24/5)x = (-9/5)x

Setting this equal to Rs. 3,240:
\[ \frac{-9}{5}x = 3,240 \]

### Step 4: Solve for x
To find x, we multiply both sides by -5/9:
\[ x = 3,240 * \left(-\frac{5}{-9}\right) = 3,240 * \frac{5}{9} \]
Calculating this gives:
\[ x = 3,240 * \frac{5}{9} = 1,800 \]

### Step 5: Calculate the Share of D
Now that we have x, we can find the share of D:
\[ D = \frac{16}{3}x = \frac{16}{3} * 1,800 \]
Calculating this gives:
\[ D = \frac{16 * 1,800}{3} = \frac{28,800}{3} = 9,600 \]

### Final Answer
The share of D is Rs. 9,600.

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