A and B together have 50,000. If 4/5th of A's amount is equal to 175th of B's how much amount B has ?

Options

A. Rs 12,500
B. Rs 40,000
C. Rs 10,000
D. Rs 20,000

Answer

To solve the problem step by step, we will define the variables, set up the equations based on the information given, and then solve for the amount that B has.

### Step 1: Define the Variables
Let:
- A's amount = x
- B's amount = y

### Step 2: Set Up the First Equation
According to the problem, A and B together have 50,000. Therefore, we can write the first equation as:
\[ x + y = 50,000 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
The problem states that 4/5th of A's amount is equal to 16/5th of B's amount. We can express this as:
\[ \frac{4}{5}x = \frac{16}{5}y \]

### Step 4: Simplify the Second Equation
To eliminate the fractions, we can multiply both sides of the equation by 5:
\[ 4x = 16y \]

### Step 5: Rearrange the Second Equation
Now, we can simplify this equation by dividing both sides by 4:
\[ x = 4y \quad \text{(Equation 2)} \]

### Step 6: Substitute Equation 2 into Equation 1
Now, we will substitute the value of x from Equation 2 into Equation 1:
\[ 4y + y = 50,000 \]

### Step 7: Combine Like Terms
Combining the terms gives us:
\[ 5y = 50,000 \]

### Step 8: Solve for y
Now, we can solve for y by dividing both sides by 5:
\[ y = \frac{50,000}{5} = 10,000 \]

### Conclusion
Thus, the amount that B has is:
\[ \text{B's amount} = 10,000 \]