Aman's expense is 30% more than Vimal's expense and Vimal's expense is 10% less than Raman's expense. If the sum of their expenses is Rs 6.447/-, then what would be the Aman's expense?

Options

A. Rs 2,200/-
B. Rs 2,457/-
C. Rs 1,890/-
D. Rs 2,100/-

Answer

To find Aman's expense, we can follow these steps:

### Step 1: Define Variables
Let Raman's expense be \( R \).
Then, Vimal's expense \( V \) can be expressed as:
\[ V = R - 0.1R = 0.9R \]
This means Vimal's expense is 10% less than Raman's expense.

### Step 2: Express Aman's Expense
Aman's expense \( A \) is 30% more than Vimal's expense, so:
\[ A = V + 0.3V = 1.3V \]
Substituting \( V \) from the previous step:
\[ A = 1.3(0.9R) = 1.17R \]

### Step 3: Write the Total Expense Equation
According to the problem, the sum of their expenses is Rs 6447:
\[ R + V + A = 6447 \]
Substituting \( V \) and \( A \):
\[ R + 0.9R + 1.17R = 6447 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ (1 + 0.9 + 1.17)R = 6447 \]
\[ 3.07R = 6447 \]

### Step 5: Solve for Raman's Expense
Now, we can solve for \( R \):
\[ R = \frac{6447}{3.07} \]

### Step 6: Calculate Raman's Expense
Calculating the value:
\[ R \approx 2100 \]

### Step 7: Calculate Vimal's Expense
Now, we can find Vimal's expense:
\[ V = 0.9R = 0.9 \times 2100 = 1890 \]

### Step 8: Calculate Aman's Expense
Finally, we can find Aman's expense:
\[ A = 1.17R = 1.17 \times 2100 \]
\[ A \approx 2457 \]

Thus, Aman's expense is **Rs 2457**.

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