A sum of ₹21000 is divided among A,B and C such that shares of A and B are in ratio of 2:3 and those of B and C are In the ratio 4:5.The amount received by B is :

Options

A. ₹6000
B. ₹4500
C. ₹7200
D. ₹8400

Answer

To solve the problem, we need to find the amount received by B when ₹21,000 is divided among A, B, and C based on the given ratios. Here’s a step-by-step solution:

### Step 1: Understand the Ratios
The shares of A and B are in the ratio of 2:3, and the shares of B and C are in the ratio of 4:5.

### Step 2: Express the Ratios
Let the share of A be 2x and the share of B be 3x (from the ratio of A to B).

For B and C, let the share of B be 4y and the share of C be 5y (from the ratio of B to C).

### Step 3: Equalize the Share of B
Since B's share is represented in both ratios, we need to make them equal. From the first ratio, we have:
- B = 3x
From the second ratio, we have:
- B = 4y

Setting these equal gives us:
3x = 4y

### Step 4: Solve for x in terms of y
From the equation 3x = 4y, we can express x in terms of y:
x = (4/3)y

### Step 5: Substitute x back into the shares
Now we can express A and C in terms of y:
- A = 2x = 2(4/3)y = (8/3)y
- B = 4y
- C = 5y

### Step 6: Write the total share equation
Now, we can sum up the shares of A, B, and C:
A + B + C = (8/3)y + 4y + 5y

To combine these, convert 4y and 5y into fractions with a common denominator:
- 4y = (12/3)y
- 5y = (15/3)y

Now, adding them together:
A + B + C = (8/3)y + (12/3)y + (15/3)y = (35/3)y

### Step 7: Set the total equal to ₹21,000
According to the problem, the total amount is ₹21,000:
(35/3)y = 21,000

### Step 8: Solve for y
To find y, multiply both sides by 3:
35y = 63,000

Now, divide by 35:
y = 63,000 / 35
y = 1,800

### Step 9: Find the share of B
Now that we have y, we can find B's share:
B = 4y = 4 * 1,800 = 7,200

### Final Answer
The amount received by B is ₹7,200.

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