Shivam's expense is `25%` more than Dharm's expense and Dharam's expense is `15%` less then Harish's expense. If the sum of the their expense is Rs 4660, then what would be the Shivam's expense?

Options

A. A)Rs 1360
B. B)Rs 1700
C. C)Rs 1600
D. D)Rs 1156

Answer

To solve the problem step by step, we will denote the expenses of Shivam, Dharam, and Harish as S, D, and H respectively.

### Step 1: Establish Relationships
1. **Shivam's Expense**: Shivam's expense is 25% more than Dharam's expense.
- This can be expressed as:
\[ S = D + 0.25D = 1.25D \]

2. **Dharam's Expense**: Dharam's expense is 15% less than Harish's expense.
- This can be expressed as:
\[ D = H - 0.15H = 0.85H \]

### Step 2: Express All Expenses in Terms of Harish's Expense
Substituting Dharam's expense into Shivam's expense:
- From \(D = 0.85H\):
\[ S = 1.25D = 1.25(0.85H) = 1.0625H \]

### Step 3: Sum of Their Expenses
According to the problem, the sum of their expenses is Rs 4660:
\[ S + D + H = 4660 \]

Substituting the expressions for S and D in terms of H:
\[ 1.0625H + 0.85H + H = 4660 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ (1.0625 + 0.85 + 1)H = 4660 \]
\[ 2.9125H = 4660 \]

### Step 5: Solve for Harish's Expense
Now, divide both sides by 2.9125 to find H:
\[ H = \frac{4660}{2.9125} \approx 1600 \]

### Step 6: Calculate Dharam's Expense
Now that we have Harish's expense, we can find Dharam's expense:
\[ D = 0.85H = 0.85 \times 1600 = 1360 \]

### Step 7: Calculate Shivam's Expense
Finally, we can find Shivam's expense using the relationship we established:
\[ S = 1.25D = 1.25 \times 1360 = 1700 \]

### Conclusion
Shivam's expense is Rs 1700.