A sum of Rs. 2130 is to be divided into three parts. The second part is `60%` of the first, and the ratio of the first to third part is `5:7`. What are the parts (in Rs.)?

Options

A. `426, 710, 994`
B. `710, 426, 994`
C. `994, 710, 426`
D. `710,994,426`

Answer

To solve the problem of dividing Rs. 2130 into three parts with the given conditions, we can follow these steps:

### Step 1: Define the Parts
Let:
- The first part be \( A \)
- The second part be \( B \)
- The third part be \( C \)

### Step 2: Establish Relationships
According to the problem:
1. The second part \( B \) is 60% of the first part \( A \):
\[ B = 0.6A \]

2. The ratio of the first part \( A \) to the third part \( C \) is given as \( 5:7 \):
\[ \frac{A}{C} = \frac{5}{7} \implies C = \frac{7}{5}A \]

### Step 3: Express Total Sum
The total sum of the parts is:
\[ A + B + C = 2130 \]

### Step 4: Substitute Relationships
Substituting \( B \) and \( C \) in terms of \( A \):
\[ A + 0.6A + \frac{7}{5}A = 2130 \]

### Step 5: Combine Like Terms
Combine the terms on the left side:
\[ A + 0.6A + 1.4A = 2130 \]
\[ 3A = 2130 \]

### Step 6: Solve for \( A \)
Now, divide both sides by 3:
\[ A = \frac{2130}{3} = 710 \]

### Step 7: Calculate \( B \) and \( C \)
Now that we have \( A \), we can find \( B \) and \( C \):
1. For \( B \):
\[ B = 0.6A = 0.6 \times 710 = 426 \]

2. For \( C \):
\[ C = \frac{7}{5}A = \frac{7}{5} \times 710 = 994 \]

### Step 8: Final Parts
Thus, the three parts are:
- First part \( A = 710 \)
- Second part \( B = 426 \)
- Third part \( C = 994 \)

### Conclusion
The parts are:
- First part: Rs. 710
- Second part: Rs. 426
- Third part: Rs. 994