Three -fifth of Aman's salary is equal to Bhavesh's salary and Seven -Eleventh of Bhavesh's Salary is equal to Charli's Salary . The sum of the salary of all of them is Rs 5559 . Which of the following is the salary of each ?

Options

A. 2805, 1683, 1071
B. 2203, 1792 , 1862
C. `2612,3122,1241`
D. 1782, 1628,1071

Answer

To solve the problem step by step, we will denote the salaries of Aman, Bhavesh, and Charlie as A, B, and C respectively.

### Step 1: Set up the equations based on the relationships given.
From the problem, we know:
1. \( \frac{3}{5} A = B \) (Three-fifth of Aman's salary is equal to Bhavesh's salary)
2. \( \frac{7}{11} B = C \) (Seven-eleventh of Bhavesh's salary is equal to Charlie's salary)
3. \( A + B + C = 5559 \) (The sum of their salaries is Rs 5559)

### Step 2: Substitute B in terms of A into the equation for C.
From the first equation, we can express B in terms of A:
\[ B = \frac{3}{5} A \]

Now, substitute B into the second equation to find C:
\[ C = \frac{7}{11} B = \frac{7}{11} \left(\frac{3}{5} A\right) = \frac{21}{55} A \]

### Step 3: Substitute B and C into the total salary equation.
Now we substitute B and C back into the total salary equation:
\[ A + B + C = 5559 \]
Substituting the values of B and C:
\[ A + \frac{3}{5} A + \frac{21}{55} A = 5559 \]

### Step 4: Find a common denominator and combine the terms.
To combine the terms, we need a common denominator. The least common multiple of 5 and 55 is 55. Thus, we rewrite the equation:
\[ A + \frac{3 \times 11}{55} A + \frac{21}{55} A = 5559 \]
This simplifies to:
\[ A + \frac{33}{55} A + \frac{21}{55} A = 5559 \]
Combining the terms gives:
\[ A + \frac{54}{55} A = 5559 \]
This can be rewritten as:
\[ \frac{55}{55} A + \frac{54}{55} A = 5559 \]
\[ \frac{109}{55} A = 5559 \]

### Step 5: Solve for A.
Now, multiply both sides by \( \frac{55}{109} \):
\[ A = 5559 \times \frac{55}{109} \]

Calculating the right side:
\[ A = 5559 \times 0.504587 = 2805 \]

### Step 6: Calculate B and C.
Now that we have A, we can find B and C:
1. For B:
\[ B = \frac{3}{5} A = \frac{3}{5} \times 2805 = 1683 \]

2. For C:
\[ C = \frac{21}{55} A = \frac{21}{55} \times 2805 = 1071 \]

### Final Salaries:
- Aman's salary (A) = Rs 2805
- Bhavesh's salary (B) = Rs 1683
- Charlie's salary (C) = Rs 1071

### Summary of Salaries:
- Aman: Rs 2805
- Bhavesh: Rs 1683
- Charlie: Rs 1071