A sum of X 7000 is divided among A,B and C in such a way that the shares of A and B are in the ratio 2 : 3 and those ofBand C are in the ratio 4: 5. The share of B is

Options

A. ? 1600
B. ? 2000
C. X 2400
D. X 3000

Answer

To find the share of B when a sum of 7000 is divided among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
We know:
- The ratio of A to B is 2:3.
- The ratio of B to C is 4:5.

### Step 2: Express the Ratios in Terms of a Common Variable
Let:
- A's share = 2x
- B's share = 3x (from the ratio A:B)

From the ratio B:C, we can express C's share in terms of B:
- B's share = 4y
- C's share = 5y

### Step 3: Equate B's Share
Since B's share is represented in two different ways (3x and 4y), we can set them equal to each other:
\[ 3x = 4y \]

### Step 4: Solve for One Variable in Terms of the Other
From the equation \( 3x = 4y \), we can express y in terms of x:
\[ y = \frac{3x}{4} \]

### Step 5: Substitute y into C's Share
Now, substitute y back into the expression for C's share:
\[ C's\ share = 5y = 5 \left(\frac{3x}{4}\right) = \frac{15x}{4} \]

### Step 6: Write the Total Share
Now we can express the total share of A, B, and C:
\[ Total = A + B + C = 2x + 3x + \frac{15x}{4} \]

### Step 7: Find a Common Denominator
To combine these, we need a common denominator (which is 4):
\[ Total = \frac{8x}{4} + \frac{12x}{4} + \frac{15x}{4} = \frac{35x}{4} \]

### Step 8: Set the Total Equal to 7000
Since the total amount is 7000, we can set up the equation:
\[ \frac{35x}{4} = 7000 \]

### Step 9: Solve for x
Multiply both sides by 4:
\[ 35x = 7000 \times 4 \]
\[ 35x = 28000 \]
Now, divide both sides by 35:
\[ x = \frac{28000}{35} = 800 \]

### Step 10: Find B's Share
Now that we have x, we can find B's share:
\[ B's\ share = 3x = 3 \times 800 = 2400 \]

### Final Answer
The share of B is **2400**.

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