Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6 ?

Options

A. A) A = 48000 B = 40000 C = 30000
B. B) A = 30000 B = 40000 C = 48000
C. C) A = 30000 B = 48000 C = 40000
D. D) A = 40000 B = 48000 C = 30000

Answer

To divide Rs. 118,000 among three persons A, B, and C in the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
We are given two ratios:
1. The ratio of A to B is 3:4.
2. The ratio of B to C is 5:6.

### Step 2: Express Ratios with a Common Variable
Let’s express the shares of A, B, and C in terms of a common variable.

- Let the share of A be \(3x\).
- Let the share of B be \(4x\) (from the ratio of A to B).
- Since B is also part of the ratio with C, we need to express B in terms of C. From the ratio of B to C (5:6), we can express B as \(5y\) and C as \(6y\).

### Step 3: Equate the Shares of B
Since both expressions represent the share of B, we can set them equal to each other:
\[ 4x = 5y \]

### Step 4: Express y in terms of x
From the equation \(4x = 5y\), we can express \(y\) in terms of \(x\):
\[ y = \frac{4x}{5} \]

### Step 5: Substitute y into C's Share
Now, substituting \(y\) into C's share:
\[ C = 6y = 6 \left(\frac{4x}{5}\right) = \frac{24x}{5} \]

### Step 6: Find Total Shares
Now we can express the total shares of A, B, and C:
\[ \text{Total} = A + B + C = 3x + 4x + \frac{24x}{5} \]

To combine these, we need a common denominator. The common denominator for \(5\) is used:
\[ = \frac{15x}{5} + \frac{20x}{5} + \frac{24x}{5} = \frac{59x}{5} \]

### Step 7: Set Total Equal to 118000
Now, we set the total equal to Rs. 118,000:
\[ \frac{59x}{5} = 118000 \]

### Step 8: Solve for x
Multiply both sides by 5:
\[ 59x = 590000 \]
Now divide by 59:
\[ x = \frac{590000}{59} = 10000 \]

### Step 9: Calculate Individual Shares
Now we can find the individual shares:
- A's share:
\[ A = 3x = 3 \times 10000 = 30000 \]
- B's share:
\[ B = 4x = 4 \times 10000 = 40000 \]
- C's share:
\[ C = \frac{24x}{5} = \frac{24 \times 10000}{5} = 48000 \]

### Final Shares
Thus, the shares are:
- A's share = Rs. 30,000
- B's share = Rs. 40,000
- C's share = Rs. 48,000