Ravi has some money with him. He give `50%` of it to Rupa and `30%` to Raje and `60%` of the remaining was donated to a charity. If he is still left with Rs. 8040, then the money the initially had was `"_________".`

Options

A. Rs. 100000
B. Rs. 100500
C. Rs. 101000
D. Rs. 101500

Explanation

To solve the problem step by step, let's denote the initial amount of money Ravi had as \( x \).

### Step 1: Calculate the amount given to Rupa
Ravi gives 50% of his money to Rupa. Therefore, the amount given to Rupa is:
\[ \text{Amount given to Rupa} = 50\% \text{ of } x = \frac{50}{100} \times x = 0.5x \]

### Step 2: Calculate the remaining amount after giving to Rupa
After giving 50% to Rupa, the remaining amount is:
\[ \text{Remaining amount after Rupa} = x - 0.5x = 0.5x \]

### Step 3: Calculate the amount given to Raje
Next, Ravi gives 30% of his initial amount \( x \) to Raje. Therefore, the amount given to Raje is:
\[ \text{Amount given to Raje} = 30\% \text{ of } x = \frac{30}{100} \times x = 0.3x \]

### Step 4: Calculate the remaining amount after giving to Raje
After giving 30% to Raje, the remaining amount is:
\[ \text{Remaining amount after Raje} = 0.5x - 0.3x = 0.2x \]

### Step 5: Calculate the amount donated to charity
Ravi donates 60% of the remaining amount to charity. Therefore, the amount donated to charity is:
\[ \text{Amount donated to charity} = 60\% \text{ of } 0.2x = \frac{60}{100} \times 0.2x = 0.12x \]

### Step 6: Calculate the remaining amount after donation
After donating to charity, the remaining amount is:
\[ \text{Remaining amount after donation} = 0.2x - 0.12x = 0.08x \]

### Step 7: Set up the equation with the remaining amount
According to the problem, Ravi is left with Rs. 8040. Therefore, we can set up the equation:
\[ 0.08x = 8040 \]

### Step 8: Solve for \( x \)
To find the initial amount \( x \), we can solve the equation:
\[ x = \frac{8040}{0.08} \]
Calculating this gives:
\[ x = 100500 \]

### Final Answer
The money Ravi initially had was Rs. 100500.

---