`(3)/(5)` th of Sarah's amount is equal to `(6)/(7)^(th)` of Priya's amount . Between them the duo has Rs 3570. How much money does priya have ?
A)Rs 1540
B)Rs 21,00
C)Rs1470
D)Rs 14,00

Options

A. Rs 1540
B. Rs 21,00
C. Rs1470
D. Rs 14,00

Answer

To solve the problem step by step, let's denote Sarah's amount as \( S \) and Priya's amount as \( P \).

### Step 1: Set up the equation based on the given information
According to the problem, we have:
\[ \frac{3}{5} S = \frac{6}{7} P \]

### Step 2: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ 3 \cdot 7 S = 6 \cdot 5 P \]
This simplifies to:
\[ 21 S = 30 P \]

### Step 3: Rearrange the equation to express \( S \) in terms of \( P \)
Now, we can express \( S \) in terms of \( P \):
\[ S = \frac{30}{21} P = \frac{10}{7} P \]

### Step 4: Use the total amount given in the problem
We know that the total amount between Sarah and Priya is Rs 3570:
\[ S + P = 3570 \]

### Step 5: Substitute \( S \) in the total amount equation
Substituting \( S \) from Step 3 into this equation:
\[ \frac{10}{7} P + P = 3570 \]

### Step 6: Combine the terms
To combine the terms, we can express \( P \) as \( \frac{7}{7} P \):
\[ \frac{10}{7} P + \frac{7}{7} P = 3570 \]
This gives us:
\[ \frac{17}{7} P = 3570 \]

### Step 7: Solve for \( P \)
To find \( P \), multiply both sides by \( \frac{7}{17} \):
\[ P = 3570 \times \frac{7}{17} \]

### Step 8: Calculate \( P \)
Calculating the right-hand side:
\[ P = 3570 \div 17 \times 7 \]
First, calculate \( 3570 \div 17 \):
\[ 3570 \div 17 = 210 \]
Now multiply by 7:
\[ P = 210 \times 7 = 1470 \]

### Conclusion
Thus, Priya has Rs 1470.