A sum of ₹4107 is divided between A, B, C and D such that the ratio of shares of A and B is 3 :4, that of B and C is 2: 1 and that of C and D is 3 : 5. The share of B is:

Options

A. ₹1443
B. ₹1003
C. ₹1223
D. ₹1332

Answer

To solve the problem of dividing ₹4107 among A, B, C, and D based on the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
We have the following ratios:
- A : B = 3 : 4
- B : C = 2 : 1
- C : D = 3 : 5

### Step 2: Express All Shares in Terms of B
From the ratios, we can express the shares of A, C, and D in terms of B:
- Let B = 4x (from A : B = 3 : 4, we can say A = 3x)
- From B : C = 2 : 1, we have C = 2x
- From C : D = 3 : 5, we can express D in terms of C. Since C = 2x, we can find D:
- If C = 2x, then D = (5/3) * C = (5/3) * 2x = (10/3)x

### Step 3: Sum of All Shares
Now, we can express the total sum of the shares:
- Total = A + B + C + D
- Total = 3x + 4x + 2x + (10/3)x

To combine these, we need a common denominator:
- Total = (9x + 12x + 6x + 10x/3)
- Total = (27x + 10x/3)

To combine these, we convert 27x to a fraction with a denominator of 3:
- Total = (81x/3 + 10x/3) = (91x/3)

### Step 4: Set Up the Equation
Now we set this equal to the total amount of money:
- (91x/3) = 4107

### Step 5: Solve for x
To find x, we multiply both sides by 3:
- 91x = 4107 * 3
- 91x = 12321

Now, divide by 91:
- x = 12321 / 91
- x = 135

### Step 6: Find the Share of B
Now that we have x, we can find the share of B:
- B = 4x = 4 * 135 = 540

### Final Answer
The share of B is ₹540.

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