A and B together have Rs. 6300.If `5/19` th of As amount is equal to `2/5` th of B's amount. The amount of 'B" is:

Options

A. Rs 2500
B. Rs 3800
C. Rs 2300
D. Rs 4000

Answer

To solve the problem step by step, let's denote A's amount as \( A \) and B's amount as \( B \).

### Step 1: Set up the equations
From the problem, we know that:
1. \( A + B = 6300 \) (Equation 1)
2. \( \frac{5}{19} A = \frac{2}{5} B \) (Equation 2)

### Step 2: Cross-multiply Equation 2
To eliminate the fractions in Equation 2, we can cross-multiply:
\[ 5 \cdot 5B = 2 \cdot 19A \]
This simplifies to:
\[ 25B = 38A \]
Now, we can express \( B \) in terms of \( A \):
\[ B = \frac{38}{25}A \quad \text{(Equation 3)} \]

### Step 3: Substitute Equation 3 into Equation 1
Now, we substitute Equation 3 into Equation 1:
\[ A + \frac{38}{25}A = 6300 \]
To combine the terms, we can express \( A \) as \( \frac{25}{25}A \):
\[ \frac{25}{25}A + \frac{38}{25}A = 6300 \]
This gives us:
\[ \frac{63}{25}A = 6300 \]

### Step 4: Solve for \( A \)
To isolate \( A \), multiply both sides by \( \frac{25}{63} \):
\[ A = 6300 \cdot \frac{25}{63} \]
Calculating this gives:
\[ A = 1000 \quad \text{(Amount of A)} \]

### Step 5: Find \( B \)
Now we can find \( B \) using Equation 1:
\[ B = 6300 - A = 6300 - 1000 = 5300 \quad \text{(Amount of B)} \]

### Final Answer
The amount of B is Rs. 5300.

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