A and B together have Rs. 1210. If 4/5 of A's amount is equal to 2/5 of B's amount, how much amount does B have?

Options

A. Rs. 460
B. Rs 484
C. Rs. 550
D. Rs. 664

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variables
Let the amount of A be \( A \) and the amount of B be \( B \). According to the problem, we know that:
\[ A + B = 1210 \]

### Step 2: Set up the equation based on the given ratio
We are given that \( \frac{4}{5} \) of A's amount is equal to \( \frac{2}{5} \) of B's amount. We can express this as:
\[ \frac{4}{5} A = \frac{2}{5} B \]

### Step 3: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the equation by 5:
\[ 4A = 2B \]

### Step 4: Rearrange the equation
Now, we can rearrange this equation to express A in terms of B:
\[ A = \frac{2}{4} B = \frac{1}{2} B \]
or equivalently,
\[ A = \frac{1}{2} B \]

### Step 5: Substitute A in the total amount equation
Now we can substitute \( A \) in the total amount equation:
\[ \frac{1}{2} B + B = 1210 \]

### Step 6: Combine like terms
Combining the terms on the left side gives:
\[ \frac{1}{2} B + \frac{2}{2} B = \frac{3}{2} B = 1210 \]

### Step 7: Solve for B
To find B, multiply both sides by \( \frac{2}{3} \):
\[ B = 1210 \times \frac{2}{3} \]
\[ B = \frac{2420}{3} \]
\[ B = 806.67 \]

### Step 8: Round to the nearest whole number
Since we are dealing with currency, we round to the nearest whole number:
\[ B \approx 807 \]

### Final Answer
Thus, the amount that B has is approximately Rs. 807.