Shuba got three fourth of whát Alka had. Alka gave half of what remained with her to Mohini. If Mohini got Rs. 625, how much did Alka have in the beginning? 

Options

A. Rs. 3750
B. Rs. 7000
C. Rs. 5000
D. Rs. 5625

Answer

To solve the problem step by step, let's define the variables and follow through the calculations:

### Step 1: Define the variable
Let \( x \) be the amount of money Alka had in the beginning.

### Step 2: Calculate how much Shuba received
According to the problem, Shuba got three-fourths of what Alka had. Therefore, the amount Shuba received can be calculated as:
\[ \text{Amount Shuba received} = \frac{3}{4}x \]

### Step 3: Calculate how much Alka has left
After giving three-fourths of her money to Shuba, the amount Alka has left is:
\[ \text{Amount Alka has left} = x - \frac{3}{4}x = \frac{1}{4}x \]

### Step 4: Determine how much Alka gave to Mohini
Alka gave half of what remained with her to Mohini. Therefore, the amount Alka gave to Mohini is:
\[ \text{Amount Alka gave to Mohini} = \frac{1}{2} \left(\frac{1}{4}x\right) = \frac{1}{8}x \]

### Step 5: Set up the equation based on the amount Mohini received
According to the problem, Mohini received Rs. 625. Therefore, we can set up the equation:
\[ \frac{1}{8}x = 625 \]

### Step 6: Solve for \( x \)
To find \( x \), we multiply both sides of the equation by 8:
\[ x = 625 \times 8 \]
Calculating the right side:
\[ x = 5000 \]

### Step 7: Conclusion
Thus, Alka had Rs. 5000 in the beginning.

### Final Answer
Alka had Rs. 5000 in the beginning.

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